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Jahn-Teller distortions of transition-metal coordination environments link orbital occupancies to structure. In the solid state, such distortions can be strongly correlated through the propagation of strain and/or through orbital interactions. Cooperative Jahn-Teller (CJT) order of this kind affects the electronic, magnetic, and structural properties of the materials in which it occurs. Conventionally studied in dense ceramics, CJT order also occurs in hybrid materials, albeit the underlying phenomenology is not well established. Here we use synchrotron powder X-ray diffraction measurements to determine links between composition and Jahn-Teller effects in a series of Prussian blue analogue (PBA) families. We develop a simple model based on the dual considerations of strain and crystal-field stabilisation that can account for the stability, extent of CJT order, and crystallite strain measured experimentally. This model shows how PBA compositions might be tuned to control the emergence and nature of CJT effects. A key implication of the model is that PBAs harbour their own complex interplay between compositional, structural, orbital, and magnetic degrees of freedom related to that of strongly-correlated functional materials such as the manganite perovskites.

We study the XXZ square lattice bilayer model with antiferromagnetic non-frustrating long-range interactions that decay as a power law with the distance. Employing large-scale high-order series expansions with classical Monte Carlo integration (pCUT+MC) about the limit of isolated Heisenberg dimers in the rung-singlet phase, we investigate the one-triplon dispersion and the corresponding spectral weight along the parameter axes of the long-range decay exponent and the XXZ anisotropy. By tuning the latter, we observe two extended regions of 3d XY and Ising universality as well as 3d Heisenberg critical exponents at the isotropic point. Along the decay exponent axis, we demonstrate mean-field behavior for strong long-range couplings, the aforementioned three universality classes for sufficiently weak interactions, and continuously varying critical exponents in-between. Using extrapolations we are able to determine the one-triplon dispersion in a quantitative fashion up to the quantum-critical breakdown of the rung-singlet phase. This allows to extract the dynamical critical exponent $z$ as a function of the decay exponent, displaying a universal behavior. The detected $z<1$ for small decay exponents is in agreement with the expected properties of the anomalous Goldstone modes in the ordered phases with broken continuous symmetry., Comment: 16 pages, 9 figures

We initiate the S-matrix bootstrap analysis of theories with non-invertible symmetries in (1+1) dimensions. Our previous work showed that crossing symmetry of S-matrices in such theories is modified, with modification characterized by the fusion category data. By imposing unitarity, symmetry and the modified crossing, we constrain the space of consistent S-matrices, identifying integrable theories with non-invertible symmetries at the cusps of allowed regions. We also extend the modified crossing rules to cases where vacua transform in non-regular representations of fusion category, utilizing a connection to a dual category $\mathscr C^{*}_{\mathscr{M}}$ and Symmetry Topological Field Theory (SymTFT). This highlights the utility of SymTFT in the analysis of scattering amplitudes., Comment: 33 pages plus appendices

We present a comprehensive study aimed at elucidating the complex magnetic correlations in Co$_2$TiSi$_{0.5}$Al$_{0.5}$ Heusler alloy having the partial B2-type structure amid L2$_1$ cubic main phase. The thermo-magnetization measurements at 100 Oe reveal the presence of two magnetic transitions at T$\rm_{C1}=278~K$ and T$\rm_{C2}=270~K$, respectively, with saturation magnetization of around 1.2 $\mu \rm_ B$/f.u. at 5~K. Our magnetic field dependent studies reveal the dominance of T$\rm_{C1}$ transition at lower fields ($\mu_0\rm H \leqslant 0.03~Tesla$); however, at higher fields the T$\rm_{C2}$ transition becomes more pronounced. The observation of remnant magnetization above Curie temperature suggests the development of Griffiths-like phase, which is extensively analyzed through {\it ac} and {\it dc}- magnetic susceptibility ($\chi$) data. The evaluation of magnetocaloric potential indicates second order phase transition with notable $\Delta S_{\rm M}=$ 2.22 Jkg$^{-1}$K$^{-1}$ at 7 Tesla. The low-field ($\mu_0\rm H \leqslant 0.1~Tesla$) magnetic entropy ($\Delta S_{\rm M}$) curves exhibit two non-identical positive peaks. The nature and range of spin interactions near T$\rm_C$ were scrutinized through rigorous critical phenomenon analysis, and the values of exponents $\alpha, \beta, \gamma$ and $\delta$ to be $0.063, 0.361, 1.108$ and $3.943$, respectively, which are found to be slightly deviating from mean-field theory towards 3D Heisenberg model. Additionally, the exchange magnetic interactions are found to decay as $J(r) \sim r^{-4.6}$. Furthermore, the density functional theory results reveal the half-metallic nature exhibiting 100\% spin polarization (SP). However, the electronic and magnetic properties are greatly affected by the incorporation of structural disorder, which results in drastic reduction of SP to mere 8.3\%., Comment: submitted

Transformer neural networks, known for their ability to recognize complex patterns in high-dimensional data, offer a promising framework for capturing many-body correlations in quantum systems. We employ an adapted Vision Transformer (ViT) architecture to model quantum impurity models, optimizing it with a subspace expansion scheme that surpasses conventional variational Monte Carlo in both accuracy and efficiency. Benchmarks against matrix product states in single- and three-orbital Anderson impurity models show that these ViT-based neural quantum states achieve comparable or superior accuracy with significantly fewer variational parameters. We further extend our approach to compute dynamical quantities by constructing a restricted excitation space that effectively captures relevant physical processes, yielding accurate core-level X-ray absorption spectra. These findings highlight the potential of ViT-based neural quantum states for accurate and efficient modeling of quantum impurity models.

In quantum physics, even simple data with a well-defined structure at the wave function level can be characterized by extremely complex correlations between its constituent elements. The inherent non-locality of the quantum correlations generally prevents one from providing their simple and transparent interpretation, which also remains a challenging problem for advanced classical techniques that approximate quantum states with neural networks. Here we show that monitoring the neural network weight space while learning quantum statistics from measurements allows to develop physical intuition about complex multipartite patterns and thus helps to construct more effective classical representations of the wave functions. Particularly, we observe the formation of distinct global convolutional structures, receptive fields in the hidden layer of the Restricted Boltzmann Machine (RBM) within the neural quantum tomography of the highly-entangled Dicke states. On this basis we propose an exact two-parameter classical representation not only for a specific quantum wave function, but for the whole family of the N-qubit Dicke states of different entanglement. Our findings suggest a fresh look at constructing convolutional neural networks for processing data with non-local patterns and pave the way for developing exact learning-based representations of entangled quantum states.

Conflicting theoretical scenarios for infinite-layer nickelate superconductors have been hotly debated, particularly regarding whether {only} a single Ni-3$d_{x^2-y^2}$ band is relevant at low energies besides electron pockets or whether multi-orbital physics including Ni-3$d_{z^2}$ is instead essential. The first scenario has emerged from density-functional theory plus dynamical mean-field theory (DFT+DMFT) calculations. Comparing the previous DFT+DMFT spectra to recent angular-resolved photoemission spectroscopy (ARPES) experiments, we find excellent agreement for both the Fermi surface and the strongly renormalized quasi-particle bands, supporting the first scenario. Our key findings further suggest that the "waterfalls" observed in ARPES might emerge from the quasi-particle--to--Hubbard-band crossover, and that additional spectral weight close to the $A$-pocket likely originates from the Ni-3$d_{xy}$ orbital., Comment: 8 pages, 4 figures

Quantum spin liquids realized in the Kitaev model offer a platform for fractionalization of spin into two quasiparticles: itinerant Majoranas and localized visons. Introducing a uniform weak magnetic field associates a Majorana zero mode with each vison excitation. The vison accompanied by a Majorana zero mode is known to behave as a non-Abelian anyon, which has garnered significant attention for its potential applications in topological quantum computing. Although spatial and temporal control of these anyons is essential for exploring their applicability in quantum computing, numerical simulations of creating, moving, and annihilating anyons by an external field remain challenging as this field violates the exact solvability of the Kitaev model. Moreover, such a field to control anyons may disturb the quantum state due to the energy injection it causes. In this study, by introducing energy dissipation phenomenologically in real-time simulations, we demonstrate that the generation, movement, and annihilation of vison excitations can be achieved while maintaining their localization. We find that a vison can be moved in a desired direction by using time-dependent local magnetic fields or gradient fields, and it remains accompanied by a Majorana zero mode even after its movement. We also reveal that a larger spatial extent of the Majorana zero modes bound to a vison facilitates the movement of the vison with smaller field gradients. Furthermore, our numerical simulations demonstrate pair creation and annihilation of visons, triggered by time-dependent magnetic fields. The results obtained in this study highlight the significance of energy dissipation in controlling non-Abelian anyons, which will stimulate further investigations into the nonequilibrium dynamics of fractional quasiparticles in strongly correlated electron systems, as well as studies for applications in quantum computation., Comment: 20 pages, 12 figures

We study the Heisenberg $S=1/2$ chain with random ferro- and antiferromagnetic couplings, using quantum Monte Carlo simulations at ultra-low temperatures, converging to the ground state. Finite-size scaling of correlation functions and excitation gaps demonstrate an exotic critical state in qualitative agreement with previous strong-disorder renormalization group calculations, but with scaling exponents depending on the coupling distribution. We find dual scaling regimes of the transverse correlations versus the distance, with an $L$ independent form $C(r)=r^{-\mu}$ for $r \ll L$ and $C(r,L)=L^{-\eta}f(r/L)$ for $r/L > 0$, where $\mu > \eta$ and the scaling function is delivered by our analysis. These results are at variance with previous spin-wave and density-matrix renormalization group calculations, thus highlighting the power of unbiased quantum Monte Carlo simulations., Comment: 8 pages, 10 figures

Waterfalls are anomalies in the angle-resolved photoemission spectrum where the energy-momentum dispersion is almost vertical, and the spectrum strongly smeared out. These anomalies are observed at relatively high energies, among others, in superconducting cuprates and nickelates. The prevalent understanding is that they originate from the coupling to some boson, with spin fluctuations and phonons being the usual suspects. Here, we show that waterfalls occur naturally in the process where a Hubbard band develops and splits off from the quasiparticle band. Our results for the Hubbard model with $\textit{ab initio}$ determined parameters well agree with waterfalls in cuprates and nickelates., Comment: 7 pages, 4 figures, 1 mp4 file

A system with a one-form global symmetry at finite temperature can be viewed as a dissipative fluid of string-like objects. In this work, we classify and construct the most general effective field theories for hydrodynamics of such string fluids, in a probe limit where the one-form charge density is decoupled from the energy-momentum tensor. We show that at leading order in the derivative expansion, there are two distinct types of diffusive transport in a string fluid depending on the discrete spacetime symmetries present in it. One particular application of interest is magnetohydrodynamics (MHD), where the effective field theories describe the diffusion of magnetic field lines. Due to the distinction between the effective field theories for different discrete symmetries, we show that the MHD of a fluid with charge conjugation symmetry is qualitatively different from that of a neutron star, which we previously discussed in arXiv:2207.01636. The explicit effective actions that we write down can be used to obtain the dispersion relations $\omega(k)$ up to cubic order in momenta for each of the different discrete symmetry choices. As another application of this formalism, we show that when the one-form symmetry is spontaneously broken, the effective action reduces to the Maxwell theory. This confirms the interpretation of the photon as a Goldstone boson arising from the spontaneous breaking of a one-form symmetry., Comment: 39 pages, 6 figures

Inducing superconducting correlations in chiral edge states is predicted to generate topologically protected zero energy modes with exotic quantum statistics. Experimental efforts to date have focused on engineering interfaces between superconducting materials, typically amorphous metals, and semiconducting quantum Hall or quantum anomalous Hall (QAH) systems. However, the strong interfacial disorder inherent can prevent the formation of isolated topological modes. An appealing alternative is to use low-density flat band materials where the ground state can be tuned between intrinsic superconducting and quantum anomalous Hall states using only the electric field effect. However, quantized transport and superconductivity have not been simultaneously achieved. Here, we show that rhombohedral tetralayer graphene aligned to a hexagonal boron nitride substrate hosts a quantized anomalous Hall state at superlattice filling $\nu = -1$ as well as a superconducting state at $\nu \approx -3.1$ at zero magnetic field. Remarkably, gate voltage can also be used to actuate nonvolatile switching of the chirality in the quantum anomalous Hall state, allowing arbitrarily reconfigurable networks of topological edge modes in locally gated devices. Thermodynamic compressibility measurements further reveal a topologically ordered fractional Chern insulator at $\nu = 2/3$, also stable at zero magnetic field, enabling proximity coupling between superconductivity and fractionally charged edge modes. Finally, we show that integrating an additional transition metal dichalcogenide layer to the heterostructure enhances the maximum superconducting critical temperature and nucleates new superconducting pockets, while leaving the topology of $\nu = -1$ the quantum anomalous Hall state intact. Our results pave the way for hybrid interfaces between superconductors and topological edge states in the low-disorder limit.

Recent experiments on nanoclusters of silver (Ag) embedded in a gold (Au) matrix reveal a huge increase in both the zero temperature resistivity and the coefficient of the ``$T$ linear'' thermal resistivity with increasing volume fraction of Ag. A fraction $f \sim 50\%$ of Ag leads to a factor of $20$ increase in the residual resistivity, and a $40$ fold enhancement in the coefficient of linear $T$ resistivity, with respect to Au. Since Au and Ag both have weak electron-phonon coupling we surmise that the huge enhancements arise from a moderately large electron-phonon coupling that may emerge at the Ag-Au interface. We construct nanocluster configurations for varying $f$ in two dimensions, define a Holstein model on it with weak coupling on the `interior' sites and a strong coupling on the interfacial sites, and solve the model through exact diagonalisation based Langevin dynamics. Computing the resistivity, we observe a large $T=0$ increase with $f$ and also a linear $T$ enhancement factor of $\sim 30$. While the enhancement factors are parameter choice dependent, our key qualitative result is that the interface physics is inhomogeneous, with widely varying distortions, and different segments of the interface dictate the residual resistivity and the thermal scattering., Comment: 6 pages, 4 figures, and Supplementary

We investigate the dynamics of multipartite entanglement after quenches from initial states which generate multiplets of quasiparticle excitations beyond the usual pair structure. We focus on the dynamics of tripartite entanglement through the lens of the Markov gap -- a computable quantity that signals irreducible tripartite entanglement when positive. In the XX spin chain, we show that the Markov gap is positive at intermediate times, implying the presence of tripartite entanglement. After a time delay, the Markov gap increases and then decays at longer times, thus exhibiting an entanglement barrier. We argue that those qualitative features are consistent with an interpretation of the spreading of tripartite entanglement by triplets of tripartite-entangled quasiparticles., Comment: 3+3 pages, 3+2 figures

The interplay between strong electron-electron interaction and symmetry breaking can have profound influence on the topological properties of materials. In magic angle twisted bilayer graphene (MATBG), the flat band with a single SU(4) flavor associated with the spin and valley degrees of freedom gains non-zero Chern number when C2z symmetry or C2zT symmetry is broken. Electron-electron interaction can further lift the SU(4) degeneracy, leading to the Chern insulator states. Here we report a complete sequence of zero-field Chern insulators at all odd integer fillings (v = +-1, +-3) with different chirality (C = 1 or -1) in hBN aligned MATBG which structurally breaks C2z symmetry. The Chern states at hole fillings (v = -1, -3), which are firstly observed in this work, host an opposite chirality compared with the electron filling scenario. By slightly doping the v = +-3 states, we have observed new correlated insulating states at incommensurate moir\'e fillings which is highly suggested to be intrinsic Wigner crystals according to our theoretical calculations. Remarkably, we have observed prominent Streda-formula violation around v = -3 state. By doping the Chern gap at v = -3 with notable number of electrons at finite magnetic field, the Hall resistance Ryx robustly quantizes to ~ h/e2 whereas longitudinal resistance Rxx vanishes, indicating that the chemical potential is pinned within a Chern gap, forming an incommensurate Chern insulator. By providing the first experimental observation of zero-field Chern insulators in the flat valence band, our work fills up the overall topological framework of MATBG with broken C2z symmetry. Our findings also demonstrate that doped topological flat band is an ideal platform to investigate exotic incommensurate correlated topological states., Comment: 28 pages. 5 figures

Non-Hermitian skin effects (NHSEs) have recently been investigated extensively at the single-particle level. When many-body interactions become dominant, novel non-Hermitian physical phenomena can emerge. In this work, we theoretically study NHSEs controlled by dissipation and interaction. We consider a 1D zigzag Bose-Hubbard lattice, subject to magnetic flux, staggered onsite single-particle loss, and uniform onsite two-particle loss. When the two-particle loss is small, two-body bound eigenstates (i.e., doublons) are all localized at the same boundary due to the interplay of the magnetic flux and staggered single-particle loss. While, for strong two-particle loss, the localization direction of doublons is unexpectedly reversed. This is attributed to the effective strong nonreciprocal hopping of doublons induced by the virtual second-order and third-order hopping processes of particle pairs with the combination of the magnetic flux, staggered single-particle loss, and strong two-particle loss. Moreover, a two-particle gain can induce the same skin-localization and reversal features of doublons, which can be utilized to dynamically observe the NHSE and its reversal of doublons controlled by interactions. Our results open up a new avenue for exploring novel non-Hermitian phenomena in many-body systems., Comment: 16 pages, 9 figures; Comments are welcome

We investigate the quantum phase transitions in strongly correlated electronic systems at $T=0^0K$ by the example of the 2D Hubbard model. The model for numerical calculations were formalized in terms of the integral equations previously obtained for the half--filled paramagnetic Hubbard model by means of the variational derivatives technique and subsequent Legendre transformation. For principal results we submit in series the momentum distribution functions $n(k)$ which display distinct attributes for the incipient regimes: the pure doublon phase, the metal phase, Weyl semimetal phase, and Weyl excitonic insulator phase at the sequential increasing the onsite Coulomb interaction $U$., Comment: 13 pages, 6 figures. arXiv admin note: text overlap with arXiv:2011.14657

We calculate the low-temperature spectral function of the symmetric single impurity Anderson model using a recently proposed dynamical exchange-correlation (xc) field formalism. The xc field, coupled to the one-particle Green's function, is obtained through analytic analysis and numerical extrapolation based on finite clusters. In the Kondo regime, the xc field consists of a complex constant term and a main quasiparticle-like oscillation term. The constant term represents the Hubbard side-band contribution, containing a bath-induced broadening effect, while the quasiparticle-like term is related to the Kondo resonance peak at low-temperature. We illustrate these features in terms of analytical and numerical calculations for small and medium-size finite clusters, and in the thermodynamic limit. The results indicate that the xc field formalism provides a good trade-off between accuracy and complexity in solving impurity problems. Consequently, it can significantly reduce the complexity of the many-body problem faced by first-principles approaches to strongly correlated materials.

We have successfully synthesized single crystals of the site-ordered cubic (C15b) Laves phase compound LuInCo$_4$ with the Co-pyrochlore sublattice for the first time. LuInCo$_4$ undergoes a ferromagnetic transition at 306 K and has a saturation moment of 3.43 $\mu_{\rm{B}}$/f.u. at 5 K. The strongly ferromagnetic nature was verified by DFT calculations, suggesting that Co-3$d$ flat bands near the Fermi level induce the spin polarization. The magnetization is isotropic above $\sim$100 K, saturates most easily in the [100] direction at low temperatures. In this anisotropic ferromagnetic state, the magnetization undergoes a metamagnetic transition in the [111] direction. Our results suggest that LuInCo$_4$ is a new strong but unusual itinerant electron ferromagnet, which deserves further study as a pyrochlore metal., Comment: 11 pages, 12 figures

The spectrum and dynamics of near-extremal black holes are strongly modified by quantum effects at low temperatures. When the extremal limit does not preserve any supersymmetry, the density of states goes to zero at extremality and no extremal black holes remain. However, when the extremal limit is supersymmetric, a large microscopic degeneracy survives and there is a gap to the first excited black hole visible from gravity. In this article we study large $N$ quantum mechanical models where supersymmetry is explicitly broken, allowing us to interpolate between these two qualitatively different pictures. We propose and analyze deformations of $\mathcal{N}=2$ SYK models with such a pattern of (super)symmetry breaking which violates the $U(1)$ $R$-symmetry. These models feature a lifting of the BPS degeneracy and a closing of the spectral gap, and we further show that the large $N$ soft effective action is given by a modification of the $\mathcal{N}=2$ Schwarzian theory in which the $U(1)_R$ mode becomes massive., Comment: 59pp

Black crystals of the mixed-valence osmate(V,VI) Sr4Os3O12 were grown via a gas phase reaction in an evacuated silica tube. The material is attracted to a permanent magnet at room temperature (295 K) but loses this property when heated or cooled. In this temperature interval, soft magnetic behavior with vanishing coercivity is observed, but the saturation magnetization is only 0.05 MuB per formula unit. Resistivity measurements show that Sr4Os3O12 is a semiconductor with a small band gap of about 0.26 eV at room temperature. X-ray diffraction on a single-crystal revealed a rhombohedral structure with the space group R-3m and lattice parameters ar = 554.64(2) pm and cr = 2700.1(1) pm at 300(1) K. The compound crystallizes in the La4Ti3O12 structure type and is isostructural to Sr4CoRe2O12. The structure is a rhombohedral stack of layered blocks, each of which can be considered as a section of three layers of the cubic perovskite structure cut perpendicular to one of its threefold axes. The Os-O-Os bond angle of about 175{/deg} favors superexchange that leads to antiferromagnetic coupling between the osmium atoms with 5d3 and 5d2 configurations. Sr4Os3O12 exhibits strong lattice dynamics. One aspect is the antiferro-rotative lattice modes of the corner-sharing [OsO6] octahedra, which freeze upon cooling. At 100 K, an ordered, yet twinned triclinic superstructure is formed. Strong spin-orbit coupling and other effects cause deformations of the [OsO6] octahedra that differ significantly at 300 K and 100 K, suggesting a change in the electronic configuration. Competing ground states could also explain the temperature dependent band gap and the magnetic fluctuations manifested in the magnetization peak at room temperature., Comment: Accepted for publication in ZAAC (9 pages and 9 figures)

In this article, we highlight our synchrotron ARPES studies of oxide thin films grown by in-situ connected MBE at beamline 5-2 of Stanford Synchrotron Radiation Lightsource (SSRL)., Comment: 8 pages, 7 figures

The multiple-spin exchange frequencies of the bilayer Wigner crystal are determined by the semiclassical method, which is asymptotically exact in the limit of dilute electron densities. The evolution of the exchange frequencies with interlayer distance -- as the crystal undergoes a sequence of structural transitions -- leads to both ferromagnetic and multi-sublattice antiferromagnetic phases. Extrapolation of the results to higher density suggests a rich magnetic phase diagram of the bilayer Wigner crystal, including the possibility of spin-nematic and valence-bond solid phases. The bilayer crystal is stable to higher electron densities than the monolayer, leading to enhanced magnetic energy scales. Our estimates of the exchange energies suggest some of the magnetic phases may be accessible in recently discovered bilayer Wigner crystals in a transition-metal dichalcogenide system., Comment: 12 pages, 17 figures

This article reviews recent progress in understanding the physics of many-body localisation (MBL) in disordered and interacting quantum many-body systems, from the perspective of ergodicity breaking on the associated Fock space. This approach to MBL is underpinned by mapping the dynamics of the many-body system onto that of a fictitious single particle on the high-dimensional, correlated and disordered Fock-space graph; yet, as we elaborate, the problem is fundamentally different from that of conventional Anderson localisation on high-dimensional or hierarchical graphs. We discuss in detail the nature of eigenstate correlations on the Fock space, both static and dynamic, and in the ergodic and many-body localised phases as well as in the vicinity of the MBL transition. The latter in turn sheds light on the nature of the transition, and motivates a scaling theory for it in terms of Fock-space based quantities. We also illustrate how these quantities can be concretely connected to real-space observables. An overview is given of several analytical and numerical techniques which have proven important in developing a comprehensive picture. Finally, we comment on some open questions in the field of MBL where the Fock-space approach is likely to prove insightful., Comment: 32 pages, 19 figures, Invited review article for J. Phys.: Condens. Matter

We study the effect of bond disorder in extended Heisenberg-Kitaev models on the honeycomb lattice, relevant for materials such as $\alpha$-RuCl$_3$, in the semiclassical limit using a combination of T-matrix and real-space spin-wave approaches. Focusing on the regime of large applied magnetic field, we discuss two distinct but related disorder-induced phenomena, namely spin textures in the vicinity of isolated impurities and magnetic excitations below the bulk gap. A finite impurity concentration smears the field-tuned phase transition and turns the isolated in-gap states into impurity bands. As a result, there is a large field regime above the bulk transition into the high-field phase where impurity-induced states fill the bulk spin gap. We illustrate the field dependence of these in-gap states for parameters relevant for $\alpha$-RuCl$_3$, and we connect our results to heat-transport and NMR data which indicated their presence.

The Kondo problem, which describes the interaction of a spin $s$ magnetic impurity with a free Fermi gas, is a classic example of strongly coupled physics. Historically, the problem has been solved by Wilson's numerical renormalization group and later by Bethe ansatz. In this paper, we present an alternate analytic solution of the Kondo problem that combines an expansion in $1/s$ with the renormalization group. We study both the case of an impurity interacting with a single channel $K=1$ of fermions in the $s \rightarrow \infty$ limit and the case with $K$ channels in the double-scaling limit $K \rightarrow \infty$, $s \to \infty$, $K/s$ fixed. Our approach allows us to describe analytically intermediate scales of the Kondo problem at large $s$ and compute thermodynamic observables such as the impurity entropy and susceptibility. We find these observables to agree with the Bethe ansatz results. We also compute the impurity spectral function, finite temperature resistivity and the Kondo screening cloud profile, properties that are not easily accessible from Bethe ansatz. Notably, in the regime $K > 2s$ we access the "non-Fermi-liquid" overscreened fixed point of the multichannel Kondo problem.

The spin-$3/2$ chain is a versatile prototypical platform for the study of competition between different kinds of magnetic orders, with the objective of obtaining a deeper understanding of the corresponding quantum phase transitions. In this work, we investigate the spin-$3/2$ chain with nearest-neighbor $J_1$, next-nearest-neighbor $J_2$, and uniaxial single-ion anisotropy $D$ terms in the absence of a magnetic field. For positive values of $J_2/J_1$ and $D/J_1$, we find seven different phases in a rich phase diagram. Without frustration $J_2=0$, a gapless Luttinger liquid phase remains stable for all $D>0$. As $J_2$ increases, we observe three phases with distinct dimerized valence bond orders, which show an intricate competition with vector chiral order and incommensurate correlations. For large $J_2$, regions of phase coexistence between the dimerized and vector chiral orders emerge. We present large-scale numerical data for the determination of transition lines, order parameters, and the nature of the phase transitions., Comment: 8 pages, 10 figures

The mechanism of CDW and its 3D structure are important fundamental issues in kagome metals. We have previously shown that, based on a 2D model, $2\times 2$ bond order (BO) emerges due to the paramagnon-interference (PMI) mechanism and that its fluctuations lead to $s$-wave superconductivity. This paper studies these issues based on realistic 3D models for kagome metals AV$_3$Sb$_5$ (A=Cs, Rb, K). We reveal that a commensurate 3D $2\times 2\times 2$ BO is caused by the PMI mechanism, by performing the 3D density-wave (DW) equation analysis for all A=Cs, Rb, K models in detail. Our results indicate a BO transition temperature $T_{\rm BO}\sim 100$K within the regime of moderate electron correlation. The 3D structure of BO is attributed to the three-dimensionality of the Fermi surface, while the 3D structure of BO is sensitively changed since the Fermi surface is quasi-2D. In the DW equation analysis, the most favorable 3D structure is (i) the alternating vertical stacking BO, where star-of-David (SoD) and tri-hexagonal (TrH) patterns stack alternatively. Other candidate is (ii) the shift-stacking BO composed of either SoD or TrH pattern. We find that the 3D structure of BO can be determined by the 3rd-order Ginzburg-Landau free energy $b\phi_1\phi_2\phi_3$. Since $b$ depends sensitively on the band structure, both (i) and (ii) can be realized. The present study enhances our understanding of the rich variety of BOs observed experimentally. It is confirmed that the PMI mechanism is the essential origin of the 3D CDW of kagome metals., Comment: 13 pages, 12 figures

We show that randomness in quadratic Hamiltonians for multimode bosonic systems results in certain information scrambling diagnostics, mirroring those seen in chaotic systems. Specifically, considering initial Gaussian states, we observe the disappearance of the memory effect in entanglement dynamics and the negative value of tripartite mutual information. However, in contrast to chaotic systems, we find that the spectral form factor exhibits a non-linear ramp and the out-of-time-ordered correlators display a power law growth. These results show that information scrambling, associated with randomness, is a distinct feature from quantum chaos. Moreover, our results provide insight into the dynamics of Gaussian states of continuous-variable systems that are useful and available resources for quantum information processing., Comment: 8+4 pages, 4+2 figures

A tight-binding model for $e_g$ orbitals on a simple cubic lattice with finite thickness is investigated. The hopping integrals for nearest-neighboring sites are considered. We examine the electronic band structures for systems with (001), (110), and (111) surfaces. Electronic states well localized around the surfaces are found for the (110) and (111) surfaces. In particular, the surface state is flat and extends in the entire Brillouin zone for the (111) surface, provided the bulk band projected onto the surface Brillouin zone is gapped. We also find that these surface states possess octupole moments in both the (110) and (111) surface cases., Comment: 7 pages, 10 figures. arXiv admin note: text overlap with arXiv:2404.00823

We derive and study a model of square planar, d8 spin crossover materials that treats elastic, magnetic and spin-orbit interactions on an equal footing. For 1D chains density matrix renormalization group calculations show that the competition between these interactions leads to six different phases. For weak spin-orbit coupling (SOC) and large antiferromagnetic interactions we find a symmetry protected topological (SPT) Haldane phase. This is equivalent to the Haldane-large-D phase transition driven by single ion anisotropy(D) in the spin-one Heisenberg model. For strong SOC the Sz=+-1 HS states are high-energy excitations. Thus, the system can be understood as a transverse field Ising model with the SOC playing the role of the transverse field. Consistent with this, we find a quantum phase transition between the THS phase and a quantum disordered (QD) phase. However, if the magnetic coupling is non-zero or the HS and LS states of a single molecule are non-degenerate the Z2 (Ising) symmetry is broken and the phase transition becomes a crossover. Thus, the QD phase and the THS phases are adiabatically connected, as, equivalently, are the large-D phase of the spin-one Heisenberg model and the quantum disordered phase of the transverse field Ising model. We also find a ferroelastic LS phase, and antierroelastic phase, with alternating HS and LS complexes, and a dimer phase, which results from the competition between antiferromagnetic and antiferroelastic interactions., Comment: 14 pages, 7 figures

Motivated by recent findings indicating high-temperature superconductivity in bilayer nickelate La$_3$Ni$_2$O$_7$ under pressures, we employ projective formalism of determinant quantum Monte Carlo simulations to explore the ground-state phase diagram and correlation effects using a simplified bilayer two-orbital Hubbard model at half filling. Our numerical results reveal the instability of the metallic phase under weak on-site Hubbard $U$, leading to the emergence of a nonmagnetic weakly insulating phase without breaking any symmetry. As the $U$ increases, an antiferromagnetic Mott insulating phase emerges when the ratio $U/t_1^x$ exceeds approximately 4.15. This magnetic phase transition belongs to the 3D O(3) Heisenberg universality class. Furthermore, using analytical continuation, we explore the dynamical properties, such as the single-particle spectral function and dynamical spin structure factor, pertinent to experimental investigations. Our numerical results can help to understand the strong correlation effects within La$_3$Ni$_2$O$_7$., Comment: 9 pages, 11 figures

We investigate the S=1/2 antiferromagnetic Heisenberg model with a 3$\times$3 checkerboard lattice structure in a longitudinal magnetic field. By using the stochastic series expansion quantum Monte Carlo (SSE-QMC) method, we obtain the properties of the non-plateau XY phase, 1/9, 3/9, 5/9, 7/9 magnetization plateau phases, and fully polarized phase. Then, we determine the precise phase transition critical points belonging to the 3D XY universality class through finite-size scaling. Moreover, we study the longitudinal and transverse dynamic spin structure factors of this model in different phases. For the non-plateau XY phase, the energy spectra present a gap between the low-energy gapless branch and the high-energy part under the competition of magnetic field and interaction. The gapless branch can be described by the spin wave theory in the canted antiferromagnetic phase of the effective "block spin" model. In the magnetization plateau phase, we identify that the excitation arises from localized disturbances within the sublattice, which are capable of spreading in momentum space. This study offers theoretical insights and interpretations for the characteristics of the ground state and the inelastic neutron scattering spectrum in two-dimensional quantum magnetic materials. Specifically, it focuses on materials with a checkerboard unit cell structure and odd-spin configurations under the influence of a longitudinal magnetic field., Comment: 11 pages, 12 figures

We explore the phase diagram of a twisted bilayer of strongly interacting electrons on a honeycomb lattice close to half-filling using the slave boson mean-field theory. Our analysis indicates that a variety of new phases can be realized as a function of chemical doping and twist angle. In particular, we find a non-magnetic excitonic insulating phase that breaks the translational symmetry of the underlying moir\'e pattern. This phase results from the interplay of strong Coulomb interactions and the twist angle. In addition, we show that the features of the renormalized dispersion such as the magic angles depend significantly on the interactions. Our results highlight the rich physics arising in doped moir\'e superlattices of Mott insulators., Comment: 18 pages, 10 figures

Recent experiments on multilayer rhombohedral graphene have unearthed a number of interesting phenomena in the regime where Integer and Fractional Quantum Anomalous Hall phenomena were previously reported. Specifically at low temperature ($T$) and low applied currents, an "Extended" Integer Quantum Anomalous Hall (EIQAH) is seen over a wide range of the phase diagram. As the current is increased, at low $T$, the EIQAH undergoes a phase transition to a metallic state at generic fillings, and to the fractional quantum anomalous Hall (FQAH) state at the Jain fillings. Increasing temperature at the Jain fillings also leads to an evolution out of the EIQAH to the Jain state. Here we provide an interpretation of these observations. We describe the EIQAH as a crystalline state (either of holes doped into the $\nu = 1$ state, or an Anomalous Hall Crystal of electrons) that breaks moir\'e translation symmetry. At generic fillings, we show how an electric current-induced depinning transition of the crystalline order leads to peculiar non-linear current-voltage curves consistent with the experiment. At Jain fillings, we propose that the depinning transition is pre-empted by an equilibrium transition between EIQAH and Jain FQAH states. This transition occurs due to the large polarizability of the Jain FQAH states which enables them to lower their energy effectively in an applied electric field compared to the crystal states. We also discuss the finite temperature evolution in terms of the relative entropies of the crystalline and FQAH states., Comment: 8+3 pages, 3 figures

Recent experimental and theoretical development in the Quantum Hall effect in monolayer graphene showed that the previous model of the valley-anisotropy interaction is incomplete, as it was assumed to be ultra-short range (USR). In this work, we use exact diagonalization to go beyond the ultra-short range to find the different phases for $\nu=2/3$. We model the interaction as Yukawa so that we can control the range as a proof of concept. Even in this simple setting, we discovered how dropping the USR condition shifts the transition borders in favour of certain phases, leads to a new bond-ordered phase appearing, and breaks the ferromagnetic phase in two competing states as a result of lifting the USR-driven degeneracy., Comment: 13 pages and 5 figures

A spin-1/2 Heisenberg model with a chirality-chirality interaction (CCI) on a two-leg ladder offers a minimal setup to study an interplay between spin and chirality degrees of freedom. This model is potentially relevant to understanding the effects of a four-spin ring exchange and a phonon-mediated interaction on a ladder. By applying the Abelian bosonization and two types of spin-chirality duality, we derive a rich phase diagram of this model that includes previously unexplored cases of a ferromagnetic rung exchange $J_\perp<0$ or a negative CCI $K_{\rm ch}<0$. The phase diagram consists of the rung singlet (RS) phase, the Haldane phase, and three non-magnetic ordered phases. Furthermore, the RS and Haldane phases consist of several regions with different dominant correlations in terms of spin, dimer, or chirality. We perform numerical simulations to confirm the predicted phase structure and critical properties., Comment: 16 pages, 13 figures. arXiv admin note: text overlap with arXiv:2311.07053

As a short topical review, this article reports progress on the generalization and applications of entanglement in non-Hermitian quantum systems. We begin by examining the realization of non-Hermitian quantum systems through the Lindblad master equation, alongside a review of typical non-Hermitian free-fermion systems that exhibit unique features. A pedagogical discussion is provided on the relationship between entanglement quantities and the correlation matrix in Hermitian systems. Building on this foundation, we focus on how entanglement concepts are extended to non-Hermitian systems from their Hermitian free-fermion counterparts, with a review of the general properties that emerge. Finally, we highlight various applications, demonstrating that entanglement entropy remains a powerful diagnostic tool for characterizing non-Hermitian physics. The entanglement spectrum also reflects the topological characteristics of non-Hermitian topological systems, while unique non-Hermitian entanglement behaviors are also discussed. The review is concluded with several future directions., Comment: a short review. 15p, 1figures

Multiple-$Q$ states as represented by a magnetic skyrmion crystal and hedgehog crystal have been extensively studied in recent years owing to their unconventional physical properties. The materials hosting multiple-$Q$ states have been so far observed in a variety of lattice structures and chemical compositions, which indicates rich stabilization mechanisms inducing the multiple-$Q$ states. We review recent developments in the research of the stabilization mechanisms of such multiple-$Q$ states with an emphasis on the microscopic spin interactions in momentum space. We show that an effective momentum-resolved spin model is a canonical model for not only understanding the microscopic origin of various multiple-$Q$ states but also exploring further exotic multiple-$Q$ states with topological properties. We introduce several key ingredients to realize the magnetic skyrmion crystal with the skyrmion numbers of one and two, hedgehog crystal, meron-antimeron crystal, bubble crystal, and other multiple-$Q$ states. We also review that the effective spin model can be used to reproduce the magnetic phase diagram in experiments efficiently., Comment: 103 pages, 22 figures, 3 tables; To appear in Materials Today Quantum

Lecture notes used as part of a graduate-level Introduction to Solid State Physics course at Cornell University. I attempt to unify and update the discussion of magnetism and superconductivity relative to standard textbook treatments, and include connections to recent research. A few related homework problems are attached at the end., Comment: 89 pages. includes homework problems

The ground state of a one-dimensional spin-1/2 uniform antiferromagnetic Heisenberg chain (AfHc) is a Tomonaga-Luttinger liquid which is quantum-critical with respect to applied magnetic fields upto a saturation field Hs beyond which it transforms to a fully polarised state. Wilson ratio has been predicted to be a good indicator for demarcating these phases [Phys. Rev. B 96, 220401 (2017)]. From detailed temperature and magnetic field dependent magnetisation, magnetic susceptibility and specific heat measurements in a metalorganic complex and comparisons with field theory and quantum transfer matrix method calculations, the complex was found to be a very good realisation of a spin-1/2 AfHc. Wilson ratio obtained from experimentally obtained magnetic susceptibility and magnetic contribution of specific heat values was used to map the magnetic phase diagram of the uniform spin-1/2 AfHc over large regions of phase space demarcating Tomonaga-Luttinger liquid, saturation field quantum critical, and fully polarised states. Luttinger parameter and spinon velocity were found to match very well with the values predicted from conformal field theory., Comment: Accepted for publication in PNAS Nexus

We study a class of many body chaotic models related to the Brownian Sachdev-Ye-Kitaev model. An emergent symmetry maps the quantum dynamics into a classical stochastic process. Thus we are able to study many dynamical properties at finite N on an arbitrary graph structure. A comprehensive study of operator size growth with or without spatial locality is presented. We will show universal behaviors emerge at large N limit, and compare them with field theory method. We also design simple stochastic processes as an intuitive way of thinking about many-body chaotic behaviors. Other properties including entanglement growth and other variants of this solvable models are discussed., Comment: 16pages + appendix

Parallel-field Hall effect is the appearance of a Hall voltage $V_{\rm H}$ that is transverse to the current $I$ when the magnetic field $B$ is applied parallel to $I$ (i.e. $B \parallel I \perp V_{\rm H}$). Such an effect is symmetry forbidden in most cases and hence is very unusual. Interestingly, the existence of a finite parallel-field Hall effect was reported for the layered topological semimetal ZrTe$_5$ and was proposed to be due to Berry curvature. However, it is forbidden for the known symmetry of ZrTe$_5$ and the possible existence of a misaligned out-of-plane magnetic field was not completely ruled out. Here, we elucidate the existence of the parallel-field Hall effect in ZrTe$_5$ with careful magnetic-field alignment. We interpret this result to originate from symmetry breaking and quantitatively explain the observed parallel-field Hall signal by considering a tilting of the Fermi surface allowed by broken symmetry., Comment: 9 pages total; 6 pages of main text with 3 figures, 3 pages of supplement with 2 figures. The raw data are available at the online depository Zenodo with the identifier 10.5281/zenodo.13350894

Control landscape phase transitions (CLPTs) occur as abrupt changes in the cost function landscape upon varying a control parameter, and can be revealed by non-analytic points in statistical order parameters. A prime example are quantum speed limits (QSL) which mark the onset of controllability as the protocol duration is increased. Here we lay the foundations of an analytical theory for CLPTs by developing Dyson, Magnus, and cumulant expansions for the cost function that capture the behavior of CLPTs with a controlled precision. Using linear and quadratic stability analysis, we reveal that CLPTs can be associated with different types of instabilities of the optimal protocol. This allows us to explicitly relate CLPTs to critical structural rearrangements in the extrema of the control landscape: utilizing path integral methods from statistical field theory, we trace back the critical scaling of the order parameter at the QSL to the topological and geometric properties of the set of optimal protocols, such as the number of connected components and its dimensionality. We verify our predictions by introducing a numerical sampling algorithm designed to explore this optimal set via a homotopic stochastic update rule. We apply this new toolbox explicitly to analyze CLPTs in the single- and two-qubit control problems whose landscapes are analytically tractable, and compare the landscapes for bang-bang and continuous protocols. Our work provides the first steps towards a systematic theory of CLPTs and paves the way for utilizing statistical field theory techniques for generic complex control landscapes., Comment: 38 pages, 24 figures

Metastable phases, in general, are unstable to nucleating droplets of the order defining the global free energy minima. However, whether such a droplet grows or shrinks relies on a competition between the surface tension and bulk energy density. We study the role of coupling a topological fermionic field to a scalar field undergoing such nucleation processes. We find that existence of non-trivial fermionic boundary modes on the nucleating droplets leads to substantial quantum corrections to the surface tension thereby modifying the size of the critical nucleus beyond which unrestricted droplet growth happens. To illustrate the phenomena we devise a minimal model of fermions in a Chern insulating system coupled to a classical Ising field in two spatial dimensions. Using a combination of analytic and numerical methods we conclusively show that topological phases can lead to characteristic quantum surface tension. Apart from material systems, our work has implications on the interplay of physics of statistical classical fields and quantum topological order., Comment: 6+2 pages, 4+2 Figures

Solitons in two-dimensional quantum field theory exhibit patterns of degeneracies and associated selection rules on scattering amplitudes. We develop a representation theory that captures these intriguing features of solitons. This representation theory is based on an algebra we refer to as the "strip algebra", $\textrm{Str}_{\mathcal{C}}(\mathcal{M})$, which is defined in terms of the non-invertible symmetry, $\mathcal{C},$ a fusion category, and its action on boundary conditions encoded by a module category, $\mathcal{M}$. The strip algebra is a $C^*$-weak Hopf algebra, a fact which can be elegantly deduced by quantizing the three-dimensional Drinfeld center TQFT, $\mathcal{Z}(\mathcal{C}),$ on a spatial manifold with corners. These structures imply that the representation category of the strip algebra is also a unitary fusion category which we identify with a dual category $\mathcal{C}_{\mathcal{M}}^{*}.$ We present a straightforward method for analyzing these representations in terms of quiver diagrams where nodes are vacua and arrows are solitons and provide examples demonstrating how the representation theory reproduces known degeneracies and selection rules of soliton scattering. Our analysis provides the general framework for analyzing non-invertible symmetry on manifolds with boundary and applies both to the case of boundaries at infinity, relevant to particle physics, and boundaries at finite distance, relevant in conformal field theory or condensed matter systems., Comment: 59 pages, 111 figures

By utilizing a multi-orbital periodic Anderson model with parameters obtained from \textit{ab initio} band structure calculations, combined with degenerate perturbation theory, we derive effective Kondo-Heisenberg and spin Hamiltonians that capture the interaction among the effective magnetic moments. This derivation encompasses fluctuations via both non-magnetic $4f^0$ and magnetic $4f^2$ virtual states, and its accuracy is confirmed through comparison with experimental data obtained from CeIn$_3$. The significant agreement observed between experimental results and theoretical predictions underscores the potential of deriving minimal models from first-principles calculations for achieving a quantitative description of $4f$ materials. Moreover, our microscopic derivation unveils the underlying origin of anisotropy in the exchange interaction between Kramers doublets, shedding light on the conditions under which this anisotropy may be weak compared to the isotropic contribution., Comment: 30 pages, 16 figures

In-plane magnetic fields offer a relatively unexplored opportunity to alter the band structure of stacks of 2D materials so that they exhibit desired physical properties. Here we show that an in-plane magnetic field combined with a transverse electric field can induce an insulator-metal (IM) transition in bilayer graphene. Our study of the magnetic response reveals that the orbital magnetic susceptibility changes from diamagnetic to paramagnetic around the transition point. We discuss several strategies to observe the IM transition, switch the diamagnetism, and more generally control the band structure of stacked 2D materials at experimentally accessible magnetic fields., Comment: 9 pages, 4 figures

We numerically study orders of planer type $(xy,x^2-y^2)$ quadrupoles on a triangular lattice with nearest-neighbor isotropic $J$ and anisotropic $K$ interactions. This type of quadrupoles possesses unique single-ion anisotropy proportional to a third order of the quadrupole moments. This provides an unconventional mechanism of triple-$q$ orders which does not exist for the degrees of freedom with odd parity under time-reversal operation such as magnetic dipoles. In addition to several single-$q$ orders, this system exhibits various orders including incommensurate triple-$q$ quasi-long-range orders and a four-sublattice triple-$q$ partial order. Our Monte-Carlo simulations demonstrate that the phase transition to the latter triple-q state belongs to the universality class of the critical line of the Ashkin-Teller model in two dimensions close to the four-state Potts class. These results indicate a possibility of realizing this unique quadrupole textures in simple triangular systems., Comment: 15 pages, 12 figures

By theoretically analyzing the recent temperature dependent transport data in pentalayer graphene [Lu et al., arXiv:2408.10203], we establish that the experimentally observed transition from low-temperature quantum anomalous Hall effect to higher-temperature fractional quantum anomalous Hall effect is a crossover phenomenon arising from the competition between interaction and disorder energy scales, with the likely zero temperature ground state of the system being either a localized insulator or a Chern insulator with a quantized anomalous Hall effect. In particular, the intriguing suppression of FQAHE in favor of QAHE with decreasing temperature is explained as arising from the low-temperature localization of the carriers where disorder overcomes the interaction effects. We provide a detailed analysis of the data in support of the crossover scenario., Comment: 8 pages, 11 figures. Comments are welcomed