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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.

While intuitive for humans, the concept of visual complexity is hard to define and quantify formally. We suggest adopting the multi-scale structural complexity (MSSC) measure, an approach that defines structural complexity of an object as the amount of dissimilarities between distinct scales in its hierarchical organization. In this work, we apply MSSC to the case of visual stimuli, using an open dataset of images with subjective complexity scores obtained from human participants (SAVOIAS). We demonstrate that MSSC correlates with subjective complexity on par with other computational complexity measures, while being more intuitive by definition, consistent across categories of images, and easier to compute. We discuss objective and subjective elements inherently present in human perception of complexity and the domains where the two are more likely to diverge. We show how the multi-scale nature of MSSC allows further investigation of complexity as it is perceived by humans., Comment: 16 pages, 11 figures, 2 tables

The analysis of empirical data through model-free inequalities leads to the conclusion that violations of Bell-type inequalities by empirical data cannot have any significance unless one believes that the universe operates according to the rules of a mathematical model., Comment: Expanded version of the paper published in Annals of Physics 469 (2024) 169742. arXiv admin note: text overlap with arXiv:2304.03962

Electronic states play a crucial role in many quantum systems of moire superlattices, quasicrystals, and fractals. As recently reported in \textit{Sierpi\'{n}ski} lattices [Phys. Rev. B 107, 115424 (2023)], the critical states are revealed by the energy level-correlation spectra, which are caused by the interplay between aperiodicity and determined self-similarity characters. In the case of the \textit{Sierpi\'{n}ski Carpet}, our results further demonstrate that there is some degree of spatial overlap between these electronic states. These states could be strongly affected by its `seed lattice' of the $generator$, and slightly modulated by the dilation pattern and the geometrical self-similarity level. These electronic states are multifractal by scaling the $q$-order inverse participation ratio or fractal dimension, which correlates with the subdiffusion behavior. In the $gene$ pattern, the averaged state-based multifractal dimension of second-order would increase as its \textit{Hausdoff dimension} increases. Our findings could potentially contribute to understanding quantum transports and single-particle quantum dynamics in fractals., Comment: 10 pages, 6 figures. Accepted by Phys. Rev. B

Correlated materials may exhibit unusually high resistivity increasing linearly in temperature, breaking through the Mott-Ioffe-Regel bound, above which coherent quasiparticles are destroyed. The fate of collective charge excitations, or plasmons, in these systems is a subject of debate. Several studies suggest plasmons are overdamped while others detect unrenormalized plasmons. Here, we present direct optical images of low-loss hyperbolic plasmon polaritons (HPPs) in the correlated van der Waals metal MoOCl2. HPPs are plasmon-photon modes that waveguide through extremely anisotropic media and are remarkably long-lived in MoOCl2. Many-body theory supported by photoemission results reveals that MoOCl2 is in an orbital-selective and highly incoherent Peierls phase. Different orbitals acquire markedly different bonding-antibonding character, producing a highly-anisotropic, isolated Fermi surface. The Fermi surface is further reconstructed and made partly incoherent by electronic interactions, renormalizing the plasma frequency. HPPs remain long-lived in spite of this, allowing us to uncover previously unseen imprints of electronic correlations on plasmonic collective modes., Comment: 32 pages, 16 figures

The presence of spin-polarized charge carriers in metallic magnets provides a mechanism for spin-lattice interactions mediated by electron-phonon coupling. Here, we present a theory of this mechanism used to estimate its effect on the exchange interactions in 2D magnets. Starting from a square lattice model at half filling, we show that the presence of electron-phonon coupling with equilibrium phonon distribution leads to a notable suppression of exchange interactions with temperature. We then apply our approach to the prototypical 2D metallic ferromagnet, Fe$_3$GeTe$_2$, with moderate electron-phonon coupling. We find that the exchange interactions undergo a renormalization, leading to a softening of the magnon modes, and suppression of the Curie temperature by $\sim$10\%. We expect that this effect can be further enhanced in systems with strong electron-phonon coupling, as well as for non-equilibrium distribution of phonons induced by strong laser fields or charge currents., Comment: 6 pages, 3 figures

Among a huge variety of known two-dimensional materials, some of them have anisotropic crystal structures; examples include so different systems as a few-layer black phoshphorus (phosphorene), beryllium nitride BeN$_4$, van der Waals magnet CrSBr, rhenium dichalgogenides ReX$_2$. As a consequence, their optical and electronic properties turn out to be highly anisotropic as well. In some cases, the anisotropy results not just in a smooth renormalization of observable properties in comparison with the isotropic case but in the appearance of dramatically new physics. The examples are hyperbolic plasmons and excitons, strongly anisotropic ordering of adatoms at the surface of two-dimensional or van der Waals materials, essential change of transport and superconducting properties. Here, we present a systematic review of electronic structure, transport and optical properties of several representative groups of anisotropic two-dimensional materials including semiconductors, anisotropic Dirac and semi-Dirac materials, as well as superconductors., Comment: Review article, 30 pages, 10 figures. Final version

We study the statistical mechanics and the equilibrium dynamics of a system of classical Heisenberg spins with frustrated interactions on a $d$-dimensional simple hypercubic lattice, in the limit of infinite dimensionality $d \to \infty$. In the analysis we consider a class of models in which the matrix of exchange constants is a linear combination of powers of the adjacency matrix. This choice leads to a special property: the Fourier transform of the exchange coupling $J(\mathbf{k})$ presents a $(d-1)$-dimensional surface of degenerate maxima in momentum space. Using the cavity method, we find that the statistical mechanics of the system presents for $d \to \infty$ a paramagnetic solution which remains locally stable at all temperatures down to $T = 0$. To investigate whether the system undergoes a glass transition we study its dynamical properties assuming a purely dissipative Langevin equation, and mapping the system to an effective single-spin problem subject to a colored Gaussian noise. The conditions under which a glass transition occurs are discussed including the possibility of a local anisotropy and a simple type of anisotropic exchange. The general results are applied explicitly to a simple model, equivalent to the isotropic Heisenberg antiferromagnet on the $d$-dimensional fcc lattice with first and second nearest-neighbour interactions tuned to the point $J_{1} = 2J_{2}$. In this model, we find a dynamical glass transition at a temperature $T_{\rm g}$ separating a high-temperature liquid phase and a low temperature vitrified phase. At the dynamical transition, the Edwards-Anderson order parameter presents a jump demonstrating a first-order phase transition., Comment: 29 pages

Using the Sierpinski gasket (triangle) and carpet (square) lattices as examples, we theoretically study the properties of fractal superconductors. For that, we focus on the phenomenon of $s$-wave superconductivity in the Hubbard model with attractive on-site potential and employ the Bogoliubov-de Gennes approach and the theory of superfluid stiffness. For the case of the Sierpinski gasket, we demonstrate that fractal geometry of the underlying crystalline lattice can be strongly beneficial for superconductivity, not only leading to a considerable increase of the critical temperature $T_c$ as compared to the regular triangular lattice but also supporting macroscopic phase coherence of the Cooper pairs. In contrast, the Sierpinski carpet geometry does not lead to pronounced effects, and we find no substantial difference as compared with the regular square lattice. We conjecture that the qualitative difference between these cases is caused by different ramification properties of the fractals., Comment: 11 pages, 24 figures; references added, a more realistic case of equilateral triangles/gaskets considered, spatial profiles of the Cooper pair density and superfluid stiffness on the square/carpet added

C$_3$N$_4$ is a recently discovered phase of carbon nitrides with the tetragonal crystal structure [D.Laniel $\textit{et al.}$, Adv. Mater. 2023, 2308030] that is stable at ambient conditions. C$_3$N$_4$ is a semiconductor exhibiting flat-band anomalies in the valence band, suggesting the emergence of many-body instabilities upon hole doping. Here, using state-of-the-art first-principles calculations we show that hole-doped C$_3$N$_4$ reveals strong electron-phonon coupling, leading to the formation of a gapped superconducting state. The phase transition temperatures turn out to be strongly dependent on the hole concentration. We propose that holes could be injected into C$_3$N$_4$ via boron doping which induces, according to our results, a rigid shift of the Fermi energy without significant modification of the electronic structure. Based on the electron-phonon coupling and Coulomb pseudopotential calculated from first principles, we conclude that the boron concentration of 6 atoms per nm$^3$ would be required to reach the critical temperature of $\sim$36 K at ambient pressure., Comment: Calculation of the Coulomb pseudopotential revised, which lowered the predicted Tc. Final version: 10 pages incl. Supplemental Material, 10 figures, and 2 tables

Magnetic skyrmions are vortex-like quasiparticles characterized by long lifetime and remarkable topological properties. That makes them a promising candidate for the role of information carriers in magnetic information storage and processing devices. Although considerable progress has been made in studying skyrmions in classical systems, little is known about the quantum case: quantum skyrmions cannot be directly observed by probing the local magnetization of the system, and the notion of topological protection is elusive in the quantum realm. Here, we explore the potential robustness of quantum skyrmions in comparison to their classical counterparts. We theoretically analyze the dynamics of a quantum skyrmion subject to local projective measurements and demonstrate that the properties of the skyrmionic quantum state change very little upon external perturbations. We further show that by performing repetitive measurements on a quantum skyrmion, it can be completely stabilized through an analog of the quantum Zeno effect., Comment: 7+eps pages, 7 figures; v2: fixed mistake in the definition of rescaled time \tau after Eq.(6)

Understanding spin-lattice interactions in antiferromagnets is one of the most fundamental issues at the core of the recently emerging and booming fields of antiferromagnetic spintronics and magnonics. Recently, coherent nonlinear spin-lattice coupling was discovered in an antiferromagnet which opened the possibility to control the nonlinear coupling strength and thus showing a novel pathway to coherently control magnon-phonon dynamics. Here, utilizing intense narrow band terahertz (THz) pulses and tunable magnetic fields up to 7 T, we experimentally realize the conditions of the Fermi magnon-phonon resonance in antiferromagnetic $CoF_{2}$. These conditions imply that both the spin and the lattice anharmonicities harvest energy transfer between the subsystems, if the magnon eigenfrequency $f_{m}$ is twice lower than the frequency of the phonon $2f_{m}=f_{ph}$. Performing THz pump-infrared probe spectroscopy in conjunction with simulations, we explore the coupled magnon-phonon dynamics in the vicinity of the Fermi-resonance and reveal the corresponding fingerprints of an impulsive THz-induced response. This study focuses on the role of nonlinearity in spin-lattice interactions, providing insights into the control of coherent magnon-phonon energy exchange.

Ultrathin CrSBr flakes are exfoliated \emph{in situ} on Au(111) and Ag(111) and their electronic structure is studied by angle-resolved photoemission spectroscopy. The thin flakes' electronic properties are drastically different from those of the bulk material and also substrate-dependent. For both substrates, a strong charge transfer to the flakes is observed, partly populating the conduction band and giving rise to a highly anisotropic Fermi contour with an Ohmic contact to the substrate. The fundamental CrSBr band gap is strongly renormalized compared to the bulk. The charge transfer to the CrSBr flake is substantially larger for Ag(111) than for Au(111), but a rigid energy shift of the chemical potential is insufficient to describe the observed band structure modifications. In particular, the Fermi contour shows a Lifshitz transition, the fundamental band gap undergoes a transition from direct on Au(111) to indirect on Ag(111) and a doping-induced symmetry breaking between the intra-layer Cr magnetic moments further modifies the band structure. Electronic structure calculations can account for non-rigid Lifshitz-type band structure changes in thin CrSBr as a function of doping and strain. In contrast to undoped bulk band structure calculations that require self-consistent $GW$ theory, the doped thin film properties are well-approximated by density functional theory if local Coulomb interactions are taken into account on the mean-field level and the charge transfer is considered.

Cubic BAs has received recent attention for its large electron and hole mobilities and large thermal conductivity. This is a rare and much desired combination in semiconductor industry: commercial semiconductors typically have high electron mobilities, or hole mobilities, or large thermal conductivities, but not all of them together. Here we report predictions from an advanced self-consistent many body perturbative theory and show that with respect to one-particle properties, BAs is strikingly similar to Si. There are some important differences, notably there is an unusually small variation in the valence band masses . With respect to two-particle properties, significant differences with Si appear. We report the excitonic spectrum for both q=0 and finite q, and show that while the direct gap in cubic BAs is about 4 eV, dark excitons can be observed down to about $\sim$1.5 eV, which may play a crucial role in application of BAs in optoelectronics., Comment: 4 pages, 2 figures

The Hubbard model provides an idealized description of electronic correlations in solids. Despite its simplicity, the model features a competition between several different phases that have made it one of the most studied systems in theoretical physics. Real materials usually deviate from the ideal of the Hubbard model in several ways, but the monolayer of Nb$_3$Cl$_8$ has recently appeared as a potentially optimal candidate for the realization of such a single-orbital Hubbard model. Here we show how this single orbital Hubbard model can be indeed constructed within a "molecular" rather than atomic basis set using ab initio constrained random phase approximation calculations. This way, we provide the essential ingredients to connect experimental reality with ab initio material descriptions and correlated electron theory, which clarifies that monolayer Nb$_3$Cl$_8$ is a Mott insulator with a gap of about 1 to 1.2eV depending on its dielectric environment. By comparing with an atomistic three-orbital model, we show that the single molecular orbital description is indeed adequate. We furthermore comment on the expected electronic and magnetic structure of the compound and show that the Mott insulating state survives in the low-temperature and bulk phases of the material., Comment: 14 pages, 7 figures, 4 tables

We take the point of view that building a one-way bridge from experimental data to mathematical models instead of the other way around avoids running into controversies resulting from attaching meaning to the symbols used in the latter. In particular, we show that adopting this view offers new perspectives for constructing mathematical models for and interpreting the results of Einstein-Podolsky-Rosen-Bohm experiments. We first prove new Bell-type inequalities constraining the values of the four correlations obtained by performing Einstein-Podolsky-Rosen-Bohm experiments under four different conditions. The proof is ``model-free'' in the sense that it does not refer to any mathematical model that one imagines to have produced the data. The constraints only depend on the number of quadruples obtained by reshuffling the data in the four data sets without changing the values of the correlations. These new inequalities reduce to model-free versions of the well-known Bell-type inequalities if the maximum fraction of quadruples is equal to one. Being model-free, a violation of the latter by experimental data implies that not all the data in the four data sets can be reshuffled to form quadruples. Furthermore, being model-free inequalities, a violation of the latter by experimental data only implies that any mathematical model assumed to produce this data does not apply. Starting from the data obtained by performing Einstein-Podolsky-Rosen-Bohm experiments, we construct instead of postulate mathematical models that describe the main features of these data. The mathematical framework of plausible reasoning is applied to reproducible and robust data, yielding without using any concept of quantum theory, the expression of the correlation for a system of two spin-1/2 objects in the singlet state. (truncated here), Comment: Corrected typo's, minor corrections in appendix B.3, major correction in section 11.4.2

In this review we discuss the latest results concerning development of the machine learning algorithms for characterization of the magnetic skyrmions that are topologically-protected magnetic textures originated from the Dzyaloshinskii-Moriya interaction that competes Heisenberg isotropic exchange in ferromagnets. We show that for classical spin systems there is a whole pool of machine approaches allowing their accurate phase classification and quantitative description on the basis of few magnetization snapshots. In turn, investigation of the quantum skyrmions is a less explored issue, since there are fundamental limitations on the simulation of such wave functions with classical supercomputers. One needs to find the ways to imitate quantum skyrmions on near-term quantum computers. In this respect, we discuss implementation of the method for estimating structural complexity of classical objects for characterization of the quantum skyrmion state on the basis of limited number of bitstrings obtained from the projective measurements.

Two-dimensional (2D) metals can host gapless plasmonic excitations, which strongly couple to electrons and thus may significantly affect superconductivity in layered materials. To investigate the dynamical interplay of the electron-electron and electron-phonon interactions in the theory of 2D superconductivity, we apply a full momentum- and frequency-dependent one-loop theory treating electron-phonon, electron-plasmon, and phonon-plasmon coupling with the same accuracy. We tune the strength of the Coulomb interaction by varying the external screening $\varepsilon_{ext}$ to the layered superconductor and find three distinct regions. At weak screening, superconductivity is mediated by plasmons. In the opposite limit conventional electron-phonon interactions dominate. In between, we find a suppressed superconducting state. Our results show that even conventional electron-phonon mediated layered superconductors can be significantly affected by the electron-plasmon coupling in a weak screening environment. This unconventional pairing contribution can then be controlled by the external screening., Comment: 12 pages, 8 figures

We explore the electronic structure of paramagnetic CrSBr by comparative first principles calculations and angle-resolved photoemission spectroscopy. We theoretically approximate the paramagnetic phase using a supercell hosting spin configurations with broken long-range order and applying quasiparticle self-consistent $GW$ theory, without and with the inclusion of excitonic vertex corrections to the screened Coulomb interaction (QS$GW$ and QS$G\hat{W}$, respectively). Comparing the quasi-particle band structure calculations to angle-resolved photoemission data collected at 200 K results in excellent agreement. This allows us to qualitatively explain the significant broadening of some bands as arising from the broken magnetic long-range order and/or electronic dispersion perpendicular to the quasi two-dimensional layers of the crystal structure. The experimental band gap at 200 K is found to be at least 1.51 eV at 200 K. At lower temperature, no photoemission data can be collected as a result of charging effects, pointing towards a significantly larger gap, which is consistent with the calculated band gap of $\approx$ 2.1 eV., Comment: 11 pages, 12 figures

We develop a strong-coupling perturbation scheme for a generic Hubbard model around a half-filled particle-hole-symmetric reference system, which is free from the fermionic sign problem. The approach is based on the lattice determinantal Quantum Monte Carlo (QMC) method in continuous and discrete time versions for large periodic clusters in a fermionic bath. Considering the first-order perturbation in the shift of the chemical potential and of the second-neighbour hopping gives an accurate electronic spectral function for a parameter range corresponding to the optimally doped cuprate system for temperature of the order of $T=0.1t$, the region hardly accessible for the straightforward lattice QMC calculations. We discuss the formation of the pseudogap and the nodal-antinodal dichotomy for a doped Hubbard system in a strong-coupling regime with the interaction parameter $U$ equal to the bandwidth and the optimal value of the next-nearest-neighbor hopping parameter $t'$ for high-temperature superconducting cuprates., Comment: 14 pages, 17 figures

Monolayer CrSBr is a recently discovered semiconducting spin-3/2 ferromagnet with a Curie temperature around 146 K. Unlike many other known two-dimensional (2D) magnets, CrSBr has an orthorhombic lattice, giving rise, for instance, to spatial anisotropy of the magnetic excitations within the 2D plane. Theoretical description of CrSBr within a spin Hamiltonian approach turns out to be nontrivial due to the triaxial magnetic anisotropy as well as due to magnetic dipolar interactions, comparable to spin-orbit effects in CrSBr. Here, we employ a Green's function formalism combined with first-principles calculations to systematically study the magnetic properties of monolayer CrSBr in different regimes of surrounding dielectric screening. We find that the magnetic anisotropy and thermodynamical properties of CrSBr depend significantly on the Coulomb interaction and its external screening. In the free-standing limit, the system turns out to be close to an easy-plane magnet, whose long-range ordering is partially suppressed. On the contrary, in the regime of large external screening, monolayer CrSBr behaves like an easy-axis ferromagnet with more stable magnetic ordering. Despite being relatively large, the magnetic dipolar interactions have only little effect on the magnetic properties. Our findings suggests that 2D CrSBr is suitable platform for studying the effects of substrate screening on magnetic ordering in low dimensions., Comment: 11 pages, 8 figures

We study intrinsic charge-carrier scattering mechanisms and determine their contribution to the transport properties of the two-dimensional ferromagnet Fe$_3$GeTe$_2$. We use state-of-the-art first-principles calculations combined with the model approaches to elucidate the role of the electron-phonon and electron-magnon interactions in the electronic transport. Our findings show that the charge carrier scattering in Fe$_3$GeTe$_2$ is dominated by the electron-phonon interaction, while the role of magnetic excitations is marginal. At the same time, the magnetic ordering is shown to effect essentially on the electron-phonon coupling and its temperature dependence. This leads to a sublinear temperature dependence of the electrical resistivity near the Curie temperature, which is in line with experimental observations. The room temperature resistivity is estimated to be $\sim$35 $\mu \Omega \cdot$cm which may be considered as an intrinsic limit for monolayer Fe$_3$GeTe$_2$., Comment: 10 pages, 8 figures

We present a new inequality constraining correlations obtained when performing Einstein-Podolsky-Rosen-Bohm experiments. The proof does not rely on mathematical models that are imagined to have produced the data and is therefore ``model-free''. The new inequality contains the model-free version of the well-known Bell-CHSH inequality as a special case. A violation of the latter implies that not all the data pairs in four data sets can be reshuffled to create quadruples. This conclusion provides a new perspective on the implications of the violation of Bell-type inequalities by experimental data., Comment: Extended version of Annals of Physics, Volume 453, 169314, 2023 (https://doi.org/10.1016/j.aop.2023.169314)

The quantum Hall (QH) effect in two-dimensional electron systems (2DESs) is conventionally observed at liquid-helium temperatures, where lattice vibrations are strongly suppressed and bulk carrier scattering is dominated by disorder. However, due to large Landau level (LL) separation (~2000 K at B = 30 T), graphene can support the QH effect up to room temperature (RT), concomitant with a non-negligible population of acoustic phonons with a wave-vector commensurate to the inverse electronic magnetic length. Here, we demonstrate that graphene encapsulated in hexagonal boron nitride (hBN) realizes a novel transport regime, where dissipation in the QH phase is governed predominantly by electron-phonon scattering. Investigating thermally-activated transport at filling factor 2 up to RT in an ensemble of back-gated devices, we show that the high B-field behaviour correlates with their zero B-field transport mobility. By this means, we extend the well-accepted notion of phonon-limited resistivity in ultra-clean graphene to a hitherto unexplored high-field realm., Comment: 17 pages, 4 figures. Supplementary information available at https://doi.org/10.1038/s41467-023-35986-3

The in-plane structural anisotropy in low-symmetric layered compound rhenium disulfide ($\text{ReS}_2$) makes it a candidate to host and tune electromagnetic phenomena specific for anisotropic media. In particular, optical anisotropy may lead to the appearance of hyperbolic plasmons, a highly desired property in optoelectronics. The necessary condition is a strong anisotropy of the principal components of the dielectric function, such that at some frequency range, one component is negative and the other is positive, i.e., one component is metallic, and the other one is dielectric. Here, we study the effect of anisotropy in $\text{ReS}_2$ and show that it can be a natural material to host hyperbolic plasmons in the ultraviolet frequency range. The operating frequency range of the hyperbolic plasmons can be tuned with the number of $\text{ReS}_2$ layers., Comment: 7 pages, 15 figures

While the pseudogap dominates the phase diagram of hole-doped cuprates, connecting the antiferromagnetic parent insulator at low doping to the strange metal at higher doping, its origin and relation to superconductivity remains unknown. In order to proceed, a complete understanding of how the single hole - initially localized in the Mott state - becomes mobile and ultimately evolves into a coherent quasiparticle at the end of the superconducting dome is required. In order to affect this development, we examine recent transport and spectroscopic studies of hole-doped cuprates across their phase diagram. In the process, we highlight a set of empirical correlations between the superfluid density and certain normal state properties of hole-doped cuprates that offer fresh insights into the emergence of metallicity within the CuO_2 plane and its influence on the robustness of the superconducting state. We conclude by arguing that the overall behavior is best understood in terms of two distinct current-carrying fluids, only one of which dominates the superconducting condensate and is gapped out below the pseudogap endpoint at a critical hole concentration p^\ast.

Two-dimensional honeycomb ferromagnets offer the unprecedented opportunity to study interactions between collective modes that in standard bulk ferromagnets do not cross paths. Indeed, they harbor an optical spin-wave branch, i.e. a spin wave which disperses weakly near the Brillouin zone center. When doped with free carriers, they also host the typical gapless plasmonic mode of 2D itinerant electron/hole systems. When the plasmon branch meets the optical spin-wave branch, energy and momentum matching occurs, paving the way for interactions between the charge and spin sector. In this Letter we present a microscopic theory of such plasmon-magnon interactions, which is based on a double random phase approximation. We comment on the possibility to unveil this physics in recently isolated 2D honeycomb magnets such as ${\rm Cr}_2{\rm Ge}_2{\rm Te}_6$., Comment: Main text: 7 pages; Supplemental Material: 10 pages

We describe a \emph{nonthermal} magnon activation mechanism in antiferromagnetic (AFM) systems via locally equilibrated \emph{spin-unpolarized} hot electrons excited by an ultrafast intense laser pulse. We employ a quantum kinetic equation that takes into account a direct electron-magnon scattering channel in either bulk AFM metal or at the interface of the AFM/normal-metal heterostructure. The mechanism is responsible for the nonequilibrium population of AFM magnon modes on a subnanosecond timescale, which are formed shortly after the local thermalization of hot electrons by Coulomb interactions. Nonequilibrium magnon populations can be additionally manipulated by applying an external magnetic field. Our work paves the way toward spin dynamics control in AFM systems via the ultrafast manipulation of out-of-equilibrium magnon excitations., Comment: 5.5 pages, 3 figures, Supplemental Material available as ancillary file

Although chromium trihalides are widely regarded as a promising class of two-dimensional magnets for next-generation devices, an accurate description of their electronic structure and magnetic interactions has proven challenging to achieve. Here, we quantify electronic excitations and spin interactions in Cr$X_3$ ($X=$~Cl, Br, I) using embedded many-body wavefunction calculations and fully generalized spin Hamiltonians. We find that the three trihalides feature comparable $d$-shell excitations, consisting of a high-spin $^4A_2$ $(t^3_{2g}e^0_{g})$ ground state lying 1.5$-$1.7 eV below the first excited state $^4T_2$ ($t^2_{2g}e^1_{g}$). CrCl$_3$ exhibits a single-ion anisotropy $A_{\rm sia} = -0.02$ meV, while the Cr spin-3/2 moments are ferromagnetically coupled through bilinear and biquadratic exchange interactions of $J_1 = -0.97$ meV and $J_2 = -0.05$ meV, respectively. The corresponding values for CrBr$_3$ and CrI$_3$ increase to $A_{\rm sia} = -0.08$ meV and $A_{\rm sia} = -0.12$ meV for the single-ion anisotropy, $J_1 = -1.21$ meV, $J_2 = -0.05$ meV and $J_1 = -1.38$ meV, $J_2 = -0.06$ meV for the exchange couplings, respectively. We find that the overall magnetic anisotropy is defined by the interplay between $A_{\rm sia}$ and $A_{\rm dip}$ due to magnetic dipole-dipole interaction that favors in-plane orientation of magnetic moments in ferromagnetic monolayers and bulk layered magnets. The competition between the two contributions sets CrCl$_3$ and CrI$_3$ as the easy-plane ($A_{\rm sia}+ A_{\rm dip} > 0$) and easy-axis ($A_{\rm sia}+ A_{\rm dip} < 0$) ferromagnets, respectively. The differences between the magnets trace back to the atomic radii of the halogen ligands and the magnitude of spin-orbit coupling. Our findings are in excellent agreement with recent experiments, thus providing reference values for the fundamental interactions in chromium trihalides., Comment: 9 pages, 2 figures, 5 tables, Supporting Information included as ancillary file

The non-trivial phase structure of the eigenstates of many-body quantum systems severely limits the applicability of quantum Monte Carlo, variational, and machine learning methods. Here, we study real-valued signful ground-state wave functions of frustrated quantum spin systems and, assuming that the tasks of finding wave function amplitudes and signs can be separated, show that the signs can be easily bootstrapped from the amplitudes. We map the problem of finding the sign structure to an auxiliary classical Ising model defined on a subset of the Hilbert space basis. We show that the Ising model does not exhibit significant frustrations even for highly frustrated parental quantum systems, and is solvable with a fully deterministic $O(K\log K)$-time combinatorial algorithm (where $K$ is the Ising model size). Given the ground state amplitudes, we reconstruct the signs of the ground states of several frustrated quantum models, thereby revealing the hidden simplicity of many-body sign structures., Comment: 11 pages, 9 figures in the main text; 9 pages, 4 figures in the supplemental information

In this report we review the method of explicit calculations of interatomic exchange interactions of magnetic materials. This involves exchange mechanisms normally referred to as Heisenberg exchange, Dzyaloshinskii-Moriya interaction and anisotropic symmetric exchange. The connection between microscopic theories of the electronic structure, such as density functional theory or dynamical mean field theory, and interatomic exchange, is given in detail. The different aspects of extracting information for an effective spin Hamiltonian that involves thousands of atoms, from electronic structure calculations considering significantly fewer atoms (1-50) is highlighted. Examples of exchange interactions of a large group of materials is presented, which involves heavy elements of the 3d period, alloys between transition metals, Heusler compounds, multilayer systems as well as overlayers and adatoms on a substrate, transition metal oxides, 4f elements, magnetic materials in two dimensions and molecular magnets. Where possible, a comparison to experimental data is made, that naturally becomes focused on the magnon dispersion. The influence of relativity is reviewed for a few cases, as is the importance of dynamical correlations. Development to theories that handle out of equilibrium conditions is also described here. The review ends with a short description of extensions of the theories behind explicit calculations of interatomic exchange, to non-magnetic situations, e.g. that describe chemical (charge) order and superconductivity.

Bulk FeSe becomes superconducting below 9\,K, but the critical temperature (T$_{c}$) is enhanced almost universally by a factor of $\sim$4-5 when it is intercalated with alkali elements. How intercalation modifies the structure is known from in-situ X-ray and neutron scattering techniques, but why T$_{c}$ changes so dramatically is not known. Here we show that there is one-to-one correspondence between the enhancement in magnetic instabilities at certain $\bf q$ vectors and superconducting pairing vertex, even while the nuclear spin relaxation rate ${1}/{(T_{1}T)}$ may not reflect this enhancement. Intercalation modifies electronic screening both in the plane and also between layers. We disentangle quantitatively how superconducting pairing vertex gains from each such changes in electronic screening. Intercalated FeSe provides an archetypal example of superconductivity where information derived from the single-particle electronic structure appears to be insufficient to account for the origins of superconductivity, even when they are computed including correlation effects. We show that the five-fold enhancement in T$_{c}$ on intercalation is not sensitive to the exact position of the d$_{xy}$ at $\Gamma$ point, as long as it stays close to E$_{F}$. Finally we show that intercalation also significantly softens the collective charge excitations, suggesting the electron-phonon interaction could play some role in intercalated FeSe., Comment: 19 pages, 8 figures

Many strongly correlated transition metal insulators are colored, even though they have large fundamental band gaps and no quasi-particle excitations in the visible range. Why such insulators possess the colors they do poses a serious challenge for any many-body theory to reliably pick up the interactions responsible for the color. We pick two archetypal cases as examples: NiO with green color and MnF\textsubscript{2} with pink color. The body of literature around the collective charge transitions (excitons) that are responsible for the color in these and other strongly correlated systems, often fail to disentangle two important factors: what makes them form and what makes them optically bright. An adequate answer requires a theoretical approach able to compute such excitations in periodic crystals, reliably and without free parameters -- a formidable challenge. We employ two kinds of advanced \emph{ab initio} many body Green's function theories to investigate both optical and spin susceptibilities. The first, a perturbative theory based on low-order extensions of the $GW$ approximation, is able to explain the color in NiO, and indeed well describe the dielectric response over the entire frequency spectrum, while the same theory is unable to explain why MnF\textsubscript{2} is pink. We show its color originates from higher order spin-flip transitions that modify the optical response. This phenomenon is not captured by low-order perturbation theory, but it is contained in dynamical mean-field theory (DMFT), which has a dynamical spin-flip vertex that contributes to the charge susceptibility. We show that symmetry lowering mechanisms, such as spin-orbit coupling, odd-parity phonons and Jan-Teller distortions, determine how `bright' these excitons are, but are not fundamental to their existence., Comment: 19 pages and 8 figures

Bistable valency in individual atoms presents a new approach toward single-atom memory, as well as a building block to create tunable and stochastic multi-well energy landscapes. Yet, this concept of orbital memory has thus far only been observed for cobalt atoms on the surface of black phosphorus, which are switched using tip-induced ionization. Here, we show that individual iron atoms on the surface of black phosphorus exhibit orbital memory using a combination of scanning tunneling microscopy and spectroscopy with ab initio calculations based on density functional theory. Unlike cobalt, the iron orbital memory can be switched in its non-ionized ground state. Based on calculations, we confirm that each iron valency has a distinct magnetic moment that is characterized by a distinguishable charge distribution due to the different orbital population. By studying the stochastic switching of the valency with varying tunneling conditions, we propose that the switching mechanism is based on a two-electron tunneling process.

We analyze the statistical mechanics of a free-standing quantum crystalline membrane within the framework of a systematic perturbative renormalization group (RG). A power-counting analysis shows that the leading singularities of correlation functions can be analyzed within an effective renormalizable model in which the kinetic energy of in-plane phonons and subleading geometrical nonlinearities in the expansion of the strain tensor are neglected. For membranes at zero temperature, governed by zero-point motion, the RG equations of the effective model provide a systematic derivation of logarithmic corrections to the bending rigidity and to the elastic Young modulus derived in earlier investigations. In the limit of a weakly applied external tension, the stress-strain relation at $T = 0$ is anomalous: the linear Hooke's law is replaced with a singular law exhibiting logarithmic corrections. For small, but finite temperatures, we use techniques of finite-size scaling to derive general relations between the zero-temperature RG flow and scaling laws of thermodynamic quantities such as the thermal expansion coefficient $\alpha$, the entropy S, and the specific heat C. A combination of the scaling relations with an analysis of thermal fluctuations shows that, for small temperatures, the thermal expansion coefficient $\alpha$ is negative and logarithmically dependent on $T$, as predicted in an earlier work. Although the requirement $\lim_{T \to 0} \alpha = 0$, expected from the third law of thermodynamics is formally satisfied, $\alpha$ is predicted to exhibit such a slow variation to remain practically constant down to unaccessibly small temperatures., Comment: 16 pages; v2: minor modifications

In narrow-band systems, correlated contribution to effective hopping becomes important, and one needs to carefully consider three types of hopping processes: between doubly and singly occupied sites, between singly occupied and empty sites, and between doubly occupied and empty or two singly occupied sites. All three hopping parameters cannot vanish simultaneously, and one should specify for which of these processes the band becomes flat. By means of exact diagonalization of finite systems we demonstrate that three hoppings play qualitatively different roles in many-body effects, in particular, in the formation of half-metallic ferromagnetic (Nagaoka) states., Comment: v3: minor corrections after acceptance for publication; v2: fix definitions of hoppings, update figures, add connection to real materials; v1: 5 pages, 1 figure in the main text, 1 figure in the supplemental information

Crystalline black nitrogen (BN) is an allotrope of nitrogen with the black phosphorus (BP) structure recently synthesized at high pressure by two independent research groups [Ji et al., Sci. Adv. 6, eaba9206 (2020); Laniel et al., Phys. Rev. Lett. 124, 216001 (2020)]. Here, we present a systematic study of the electronic and optical properties of BN focusing on its comparison with BP. To this end, we use the state-of-the-art quasiparticle self-consistent $GW$ approach with vertex corrections in both the electronic and optical channels. Despite many similarities, the properties of BN are found to be considerably different. Unlike BP, BN exhibits a larger optical gap (2.5 vs 0.26 eV), making BN transparent in the visible spectral region with a highly anisotropic optical response. This difference can be primarily attributed to a considerably reduced dielectric screening in BN, leading to enhancement of the effective Coulomb interaction. Despite relatively strong Coulomb interaction, exciton formation is largely suppressed in both materials. Our analysis of the elastic properties shows exceptionally high stiffness of BN, comparable to that of diamond., Comment: Final version; 10 pages, 9 figures, 6 tables

We outline a phenomenological theory of evolution and origin of life by combining the formalism of classical thermodynamics with a statistical description of learning. The maximum entropy principle constrained by the requirement for minimization of the loss function is employed to derive a canonical ensemble of organisms (population), the corresponding partition function (macroscopic counterpart of fitness) and free energy (macroscopic counterpart of additive fitness). We further define the biological counterparts of temperature (biological temperature) as the measure of stochasticity of the evolutionary process and of chemical potential (evolutionary potential) as the amount of evolutionary work required to add a new trainable variable (such as an additional gene) to the evolving system. We then develop a phenomenological approach to the description of evolution, which involves modeling the grand potential as a function of the biological temperature and evolutionary potential. We demonstrate how this phenomenological approach can be used to study the "ideal mutation" model of evolution and its generalizations. Finally, we show that, within this thermodynamics framework, major transitions in evolution, such as the transition from an ensemble of molecules to an ensemble of organisms, that is, the origin of life, can be modeled as a special case of bona fide physical phase transitions that are associated with the emergence of a new type of grand canonical ensemble and the corresponding new level of description, Comment: 23 pages

We apply the theory of learning to physically renormalizable systems in an attempt to develop a theory of biological evolution, including the origin of life, as multilevel learning. We formulate seven fundamental principles of evolution that appear to be necessary and sufficient to render a universe observable and show that they entail the major features of biological evolution, including replication and natural selection. These principles also follow naturally from the theory of learning. We formulate the theory of evolution using the mathematical framework of neural networks, which provides for detailed analysis of evolutionary phenomena. To demonstrate the potential of the proposed theoretical framework, we derive a generalized version of the Central Dogma of molecular biology by analyzing the flow of information during learning (back-propagation) and predicting (forward-propagation) the environment by evolving organisms. The more complex evolutionary phenomena, such as major transitions in evolution, in particular, the origin of life, have to be analyzed in the thermodynamic limit, which is described in detail in the accompanying paper., Comment: 29 pages, 3 figures

Excitons with large binding energies $\sim$2-3 eV in CrX$_{3}$ are historically characterized as being localized (Frenkel) excitons that emerge from the atomic $d{-}d$ transitions between the Cr-3$d$-$t_{2g}$ and $e_{g}$ orbitals. The argument has gathered strength in recent years as the excitons in recently made monolayers are found at almost the same energies as the bulk. The Laporte rule, which restricts such parity forbidden atomic transitions, can relax if, at least, one element is present: spin-orbit coupling, odd-parity phonons or Jahn-Teller distortion. While what can be classified as a purely Frenkel exciton is a matter of definition, we show using an advanced first principles parameter-free approach that these excitons in CrX$_{3}$, in both its bulk and monolayer variants, have band-origin and do not require the relaxation of Laporte rule as a fundamental principle. We show that, the character of these excitons is mostly determined by the Cr-$d$ orbital manifold, nevertheless, they appear only as a consequence of X-p states hybridizing with the Cr-$d$. The hybridization enhances as the halogen atom becomes heavier, bringing the X-$p$ states closer to the Cr-$d$ states in the sequence Cl{\textrightarrow}Br{\textrightarrow}I, with an attendant increase in exciton intensity and decrease in binding energy. By applying a range of different kinds of perturbations, we show that, moderate changes to the two-particle Hamiltonian that essentially modifies the Cr-$d$-X-$p$ hybridization, can alter both the intensities and positions of the exciton peaks. A detailed analysis of several deep lying excitons, with and without strain, reveals that the exciton is most Frenkel like in CrCl$_{3}$ and acquires mixed Frenkel-Wannier character in CrI$_{3}$., Comment: 17 pages, 12 figures

Ordered mesoscale structures in 2D materials induced by small misorientations have opened pathways for a wide variety of novel electronic, ferroelectric, and quantum phenomena. Until now, the only mechanism to induce this periodic ordering was via mechanical rotations between the layers, with the periodicity of the resulting moir\'e pattern being directly related to twist angle. Here we report a fundamentally new mechanism for emergence of mesoscopic periodic patterns in multilayer sulfur-containing metal phosphorous trichalcogenide, MnPS$_{3}$, induced by the electron beam. The formation under the beam of periodic hexagonal patterns with several characteristic length scales, nucleation and transitions between the phases, and local dynamics are demonstrated. The associated mechanisms are attributed to the relative contraction of the layers caused by beam-induced sulphur vacancy formation with subsequent ordering and lattice parameter change. As a result, the plasmonic response of the system is locally altered, suggesting an element of control over plasmon resonances by electron beam patterning. We pose that harnessing this phenomenon provides both insight into fundamental physics of quantum materials and opens a pathway towards device applications by enabling controlled periodic potentials on the atomic scale., Comment: Electron microscopy data and analysis codes are freely available here: https://github.com/kevinroccapriore/MnPS3

Finding out how symmetry encodes optical polarization information into the selection rule in molecules and materials is important for their optoelectronic applications including spectroscopic analysis, display technology and quantum computation. Here, we extend the polarization-dependent selection rules from atoms to solid systems with point group descriptions via rotational operator for circular polarization and $2$-fold rotational operator (or reflection operator) for linear polarization. As a variant of graphene quantum dot (GQD), twisted bilayer graphene quantum dot (TBGQD) certainly inherits GQD's advantages including ultrathin thickness, excellent biocompatibility and shape- and size-tunable optical absorption/emission. We then naturally ask how the electronic structures and optical properties of TBGQDs rely on size, shape, twist angle and correlation effects. We build plentiful types of TBGQDs with $10$ point groups and obtain the optical selection rule database for all types, where the current operator matrix elements identify the generalized polarization-dependent selection rules. Our results show that both of the electronic and optical band gaps follow power-law scalings and the twist angle has the dominant role in modifying the size scaling. We map an atlas of optical conductivity spectra for both size and twist angle in TBGQDs. As a result of quantum confinement effect of finite size, in the atlas a new type of optical conductivity peaks absent in twisted bilayer graphene bulk is predicted theoretically with multiple discrete absorption frequencies from infrared to ultraviolet light, enabling applications on photovoltaic devices and photodetectors. The atlas and size scaling provide a full structure/symmetry-function interrelation and hence offers an excellent geometrical manipulation of optical properties of TBGQD as a building block in integrated carbon optoelectronics.

Epitaxial semiconductor-superconductor heterostructures are promising as a platform for gate-tunable superconducting electronics. Thus far, the superconducting properties in such hybrid systems have been predicted based on simplified hybridization models which neglect the electronic structure that can arise at the interface. Here, we demonstrate that the hybrid electronic structure derived at the interface between semiconducting black phosphorus and atomically thin films of lead can drastically modify the superconducting properties of the thin metallic film. Using ultra-low temperature scanning tunneling microscopy and spectroscopy, we ascertain the moir\'e structure driven by the interface, and observe a strongly anisotropic renormalization of the superconducting gap and vortex structure of the lead film. Based on density functional theory, we attribute the renormalization of the superconductivity to weak hybridization at the interface where the anisotropic characteristics of the semiconductor band structure is imprinted on the Fermi surface of the superconductor. Based on a hybrid two-band model, we link this hybridization-driven renormalization to a weighting of the superconducting order parameter that quantitatively reproduces the measured spectra. These results illustrate the effect of interfacial hybridization at superconductor-semiconductor heterostructures, and pathways for engineering quantum technologies based on gate-tunable superconducting electronics.