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We study the boundary criticality enriched by boundary fermions, which ubiquitously emerge in topological phases of matter, with a focus on topological insulators and topological superconductors. By employing dimensional regularization and bosonization techniques, we uncover several unprecedented boundary universality classes. These include the boundary Gross-Neveu-Yukawa critical point and the special Berezinskii-Kosterlitz-Thouless (BKT) transition, both resulting from the interplay between edge modes and bulk bosons. We present a comprehensive sketch of the phase diagram that accommodates these boundary criticalities and delineate their critical exponents. Additionally, we explore a 1+1D conformal defect decorated with fermions, where a defect BKT transition is highlighted. We conclude with a discussion on potential experimental realizations of these phenomena., Comment: 4.4 pages + supplemental material, 2 figures, 1 table

The coupling between defects and extended critical degrees of freedom gives rise to the intriguing theory known as defect conformal field theory (CFT). In this work, we introduce a novel family of boundary and interface CFTs by coupling $N$ Majorana chains with SYK$_q$ interactions at the defect. Our analysis reveals that the interaction with $q=2$ constitutes a new marginal defect. Employing a versatile saddle point method, we compute unique entanglement characterizations, including the $g$-function and effective central charge, of the defect CFT. Furthermore, we analytically evaluate the transmission coefficient using CFT techniques. Surprisingly, the transmission coefficient deviates from the universal relation with the effective central charge across the defect at the large $N$ limit, suggesting that our defect CFT extends beyond all known examples of Gaussian defect CFT., Comment: 15 pages, 6 figures

The widely-used Kohn-Sham implementation of density functional theory (DFT) maps a system of interacting electrons onto an auxiliary non-interacting one and is presumably inaccurate for strongly correlated materials. We present a concrete benchmark for DFT by examining the electronic ground state phase diagram of a strongly interacting chain with uneven, non-integer nuclear charges. The interplay between charge imbalance and Coulomb repulsion yields two competing phases, a band insulator and a Mott insulator. By including infinitesimal lattice distortions, DFT stabilizes the intermediate spontaneously dimerized insulator phase that results from this competition. We assess the phase diagram by mapping the bond length and nuclear charge ratio of the chain to the ionic Hubbard model and performing highly accurate density matrix renormalization group calculations. Our comparative study provides foundational insight into the utility of symmetry-broken DFT as a predictive tool for elucidating phase diagrams with competing orders.

Quantum entanglement marks a definitive feature of topological states. However, the entanglement spectrum remains insufficiently explored for topological states without a bulk energy gap. Using a combination of field theory and numerical techniques, we accurately calculate and analyze the entanglement spectrum of gapless symmetry protected topological states in one dimension. We highlight that the universal entanglement spectrum not only encodes the nontrivial edge degeneracy, generalizing the Li-Haldane conjecture to gapless topological states, but also contains the operator content of the underlying boundary conformal field theory. This implies that the bulk wave function can act as a fingerprint of both quantum criticality and topology in gapless symmetry protected topological states. We also identify a symmetry enriched conformal boundary condition that goes beyond the conventional conformal boundary condition., Comment: 4.5 pages with supplemental materials, 10 figures

The presence of quantum noises inherent to real physical systems can strongly impact the physics in hybrid quantum circuits with local random unitaries and mid-circuit measurements. The quantum noises with a size-independent occurring probability can lead to the disappearance of a measurement-induced entanglement phase transition and the emergence of a single area-law phase. In this work, we investigate the effects of quantum noises with size-dependent probabilities $q=p/L^{\alpha}$ where $\alpha$ represents the scaling exponent. We have identified a noise-induced entanglement phase transition from a volume law to a power (area) law in the presence (absence) of measurements as $p$ increases when $\alpha=1$. With the help of an effective statistical model, we reveal that the phase transition is of first-order arising from the competition between two types of spin configurations and shares the same analytical understanding as the noise-induced coding transition. This unified picture further deepens the understanding of the connection between entanglement behavior and the capacity of information protection. When $\alpha \neq 1$, one spin configuration always dominates regardless of $p$ and thus the phase transition disappears. Moreover, we highlight the difference between the effects of size-dependent bulk noise and boundary noises. We validate our analytical predictions with extensive numerical results from stabilizer circuit simulations., Comment: 11 pages, 18 figures

We investigate the evolution of entanglement within an open, strongly coupled system interacting with a heat bath as its environment, in the frameworks of both the doubly holographic model and the Sachdev-Ye-Kitaev (SYK) model. Generally, the entanglement within the system initially increases due to internal interactions; however, it eventually dissipates into the environment. In the doubly holographic setup, we consider an end-of-the-world brane in the bulk to represent an eternal black hole coupled with its radiation and the evolution of the global thermofield double (TFD) state. For small black holes, the reflected entropy between the bipartition exhibits a ramp-plateau-slump behavior, where the plateau arises due to the phase transition of the entanglement wedge cross-section before the Page time. Similarly, the mutual information between the bipartition displays a ramp-slop-stabilizing behavior. In quantum mechanics, we consider a double copy of the SYK-plus-bath system in a global TFD state, resembling an eternal black hole interacting with an environment. The R\'enyi mutual information within the double-copied SYK clusters exhibits a ramp-plateau-slope-stabilizing behavior. The dynamic behaviors of the entanglement quantities observed in these two models are attributable to the competition between the internal interaction of the system and the external interaction with the baths. Our study provides a fine-grained picture of the entanglement dynamics inside black holes before their Page time., Comment: 31 pages, 10 figures, major revision, published version

Quantum electrodynamics (QED) is a cornerstone of particle physics and also finds diverse applications in condensed matter systems. Despite its significance, the dynamics of quantum electrodynamics under a quantum quench remains inadequately explored. In this paper, we investigate the nonequilibrium regime of quantum electrodynamics following a global quantum quench. Specifically, a massive Dirac fermion is quenched to a gapless state with an interaction with gauge bosons. In stark contrast to equilibrium (3+1)-dimensional QED with gapless Dirac fermions, where the coupling is marginally irrelevant, we identify a nonequilibrium fixed point characterized by nonFermi liquid behavior. Notably, the anomalous dimension at this fixed point varies with the initial quench parameter, suggesting an interesting quantum memory effect in a strongly interacting system. Additionally, we propose distinctive experimental signatures for nonequilibrium quantum electrodynamics., Comment: 15 pages, 7 figures

Deconfined quantum criticality (DQC) arises from fractionalization of quasi-particles and leads to fascinating behaviors beyond the Landau-Ginzburg-Wilson (LGW) description of phase transitions. The unusual aspects of DQC in equilibrium also suggest exotic phenomena out of equilibrium, which are still largely unexplored. Here we study manifestations of DQC when driving (quantum annealing) a two-dimensional quantum magnet through a critical point separating antiferromagnetic and spontaneously dimerized ground states. Numerical simulations show that the celebrated Kibble-Zurek scaling (KZS) mechanism is inadequate for describing the annealing process. To explain our results, we introduce the concept of dual asymmetric KZS, where a deconfinement time enters in addition to the conventional relaxation time and the scaling also depends on the direction in which the system is driven through the critical point according to a duality principle connecting the topological defects in the two phases. These defects -- spinons in the dimerized phase and space-time hedgehogs in the antiferromagnetic phase -- require a much longer time scale for equilibration than the amplitude of the order parameter. Beyond the new insights into DQC, our scaling approach provides a new window into out-of-equilibrium criticality with multiple length and time scales., Comment: 15 pages, 9 figures

Krylov complexity measures the spread of the wavefunction in the Krylov basis, which is constructed using the Hamiltonian and an initial state. We investigate the evolution of the maximally entangled state in the Krylov basis for both chaotic and non-chaotic systems. For this purpose, we derive an Ehrenfest theorem for the Krylov complexity, which reveals its close relation to the spectrum. Our findings suggest that neither the linear growth nor the saturation of Krylov complexity is necessarily associated with chaos. However, for chaotic systems, we observe a universal rise-slope-ramp-plateau behavior in the transition probability from the initial state to one of the Krylov basis states. Moreover, a long ramp in the transition probability is a signal for spectral rigidity, characterizing quantum chaos. Also, this ramp is directly responsible for the late-time peak of Krylov complexity observed in the literature. On the other hand, for non-chaotic systems, this long ramp is absent. Therefore, our results help to clarify which features of the wave function time evolution in Krylov space characterize chaos. We exemplify this by considering the Sachdev-Ye-Kitaev model with two-body or four-body interactions., Comment: 40+26 pages, 19 figures, major revision, published version

Finding new critical states of matter is an important subject in modern many-body physics. Here we study the effect of measurement and postselection on the critical ground state of a Luttinger liquid theory and show that it can lead to qualitatively new critical states. Depending on the Luttinger parameter $K$, the effect of measurement is irrelevant (relevant) at $K>1$ ($K<1$). We reveal that this causes an entanglement transition between two phases, one with logarithmic entanglement entropy for a subregion ($K>1$), and the other with algebraic entanglement entropy ($K<1$). At the critical point $K=1$, the measurement is marginal, and we find new critical states whose entanglement entropy exhibits a logarithmic behavior with a continuous effective central charge as a function of measurement strength. We also performed numerical density matrix renormalization group and fermionic Gaussian state simulations to support our results. We further discuss promising and feasible routes to experimentally realize new critical states in our work., Comment: 4.7 pages + supplemental material, 4 figures; updated variational quantum algorithms

We study the effect of disorder on the spacetime supersymmetry that is proposed to emerge at the quantum critical point of pair density wave transition in (2+1)D Dirac semimetals and (3+1)D Weyl semimetals. In the (2+1)D Dirac semimetal, we consider three types of disorder, including random scalar potential, random vector potential and random mass potential, while the random mass disorder is absent in the (3+1)D Weyl semimetal. Via a systematic renormalization group analysis, we find that any type of weak random disorder is irrelevant due to the couplings between the disorder potential and the Yukawa vertex. The emergent supersymmetry is thus stable for weak random potentials. Our work will pave the way for exploration supersymmetry in realistic condensed matter systems.

Unidirectional transport and localized cyclotron motion are two opposite physical phenomena. Here, we study the interplay effects between them on nonreciprocal lattices subject to a magnetic field. We show that, in the long-wavelength limit, the trajectories of the wave packets always form closed orbits in four-dimensional (4D) complex space. Therefore, the semiclassical quantization rules persist despite the nonreciprocity, which preserves real Landau levels. We predict a different type of non-Hermitian spectral transition induced by the spontaneous breaking of the combined mirror-time reversal ($\mathcal{MT}$) symmetry, which generally exists in such systems. An order parameter is proposed to describe the $\mathcal{MT}$ phase transition, not only to determine the $\mathcal{MT}$ phase boundary but also to quantify the degree of $\mathcal{MT}$-symmetry breaking. Such an order parameter can be generally applied to all types of non-Hermitian phase transitions., Comment: 18 pages, including supplemental material, major revision, the version to be published in PRB Letter

We develop solvable models of large-$N$ hybrid quantum circuits on qubits and fermions with long-range power-law interactions and continuous local monitoring, which provide analytical access to the entanglement phase diagram and error-correcting properties of many-body entangled non-equilibrium states generated by such dynamics. In one dimension, the long-range coupling is irrelevant for $\alpha>3/2$, where $\alpha$ is the power-law exponent, and the models exhibit a conventional measurement-induced phase transition between volume- and area-law entangled phases. For $1/2<\alpha<3/2$ the long-range coupling becomes relevant, leading to a nontrivial dynamical exponent at the measurement-induced phase transition. More interestingly, for $\alpha<1$ the entanglement pattern receives a sub-volume correction for both area-law and volume-law phases, indicating that the phase realizes a quantum error correcting code whose code distance scales as $L^{2-2\alpha}$. While the entanglement phase diagram is the same for both the interacting qubit and fermionic hybrid Brownian circuits, we find that long-range free-fermionic circuits exhibit a distinct phase diagram with two different fractal entangled phases., Comment: 8+12 pages, 6 figures, v2 close to published version

We study the entanglement transition in monitored Brownian SYK chains in the large-$N$ limit. Without measurement the steady state $n$-th R\'enyi entropy is obtained by summing over a class of solutions, and is found to saturate to the Page value in the $n\rightarrow 1$ limit. In the presence of measurements, the analytical continuation $n\rightarrow 1$ is performed using the cyclic symmetric solution. The result shows that as the monitoring rate increases, a continuous von Neumann entanglement entropy transition from volume-law to area-law occurs at the point of replica symmetry unbreaking., Comment: 33 pages, 3 figures

We investigate the effect of quantum errors on a monitored Brownian Sachdev-Ye-Kitaev (SYK) model featuring a measurement-induced phase transition that can be understood as a symmetry-breaking transition of an effective $Z_4$ magnet in the replica space. The errors describe the loss of information about the measurement outcomes and are applied during the non-unitary evolution or at the end of the evolution. In the former case, we find that this error can be mapped to an emergent magnetic field in the $Z_4$ magnet, and as a consequence, the symmetry is explicitly broken independent of the measurement rate. R\'enyi entropies computed by twisting boundary conditions now generate domain walls even in the would-be symmetric phase at a high measurement rate. The entropy is therefore volume-law irrespective of the measurement rate. In the latter case, the error-induced magnetic field only exists near the boundary of the magnet. Varying the magnetic field leads to a pinning transition of domain walls, corresponding to error threshold of the quantum code prepared by the non-unitary SYK dynamics., Comment: 4.4 pages + supplemental material, 4 figures

Non-unitary evolution can give rise to novel steady states classified by their entanglement properties. In this work, we aim to understand its interplay with long-range hopping that decays with $r^{-\alpha}$ in free-fermion systems. We first study two solvable Brownian models with long-range non-unitary dynamics: a large-$N$ SYK$_2$ chain and a single-flavor fermion chain and we show that they share the same phase diagram. When $\alpha>0.5$, we observe two critical phases with subvolume entanglement scaling: (i) $\alpha>1.5$, a logarithmic phase with dynamical exponent $z=1$ and logarithmic subsystem entanglement, and (ii) $0.5<\alpha<1.5$, a fractal phase with $z=\frac{2\alpha-1}{2}$ and subsystem entanglement $S_A\propto L_A^{1-z}$, where $L_A$ is the length of the subsystem $A$. These two phases cannot be distinguished by the purification dynamics, in which the entropy always decays as $L/T$. We then confirm that the results are also valid for the static SYK$_2$ chain, indicating the phase diagram is universal for general free-fermion systems. We also discuss phase diagrams in higher dimensions and the implication in measurement-induced phase transitions., Comment: 17 pages, 5 figures

We construct Brownian Sachdev-Ye-Kitaev (SYK) chains subjected to continuous monitoring and explore possible entanglement phase transitions therein. We analytically derive the effective action in the large-$N$ limit and show that an entanglement transition is caused by the symmetry breaking in the enlarged replica space. In the noninteracting case with SYK$_2$ chains, the model features a continuous $O(2)$ symmetry between two replicas and a transition corresponding to spontaneous breaking of that symmetry upon varying the measurement rate. In the symmetry broken phase at low measurement rate, the emergent replica criticality associated with the Goldstone mode leads to a log-scaling entanglement entropy that can be attributed to the free energy of vortices. In the symmetric phase at higher measurement rate, the entanglement entropy obeys area-law scaling. In the interacting case, the continuous $O(2)$ symmetry is explicitly lowered to a discrete $C_4$ symmetry, giving rise to volume-law entanglement entropy in the symmetry-broken phase due to the enhanced linear free energy cost of domain walls compared to vortices. The interacting transition is described by $C_4$ symmetry breaking. We also verify the large-$N$ critical exponents by numerically solving the Schwinger-Dyson equation., Comment: 4.5 pages + supplemental material, 4 figures

Recently, the steady states of non-unitary free fermion dynamics are found to exhibit novel critical phases with power-law squared correlations and a logarithmic subsystem entanglement. In this work, we theoretically understand the underlying physics by constructing solvable static/Brownian quadratic Sachdev-Ye-Kitaev chains with non-Hermitian dynamics. We find the action of the replicated system generally shows (one or infinite copies of) ${O(2)\times O(2)}$ symmetries, which is broken to ${O(2)}$ by the saddle-point solution. This leads to an emergent conformal field theory of the Goldstone modes. We derive the effective action and obtain the universal critical behaviors of squared correlators. Furthermore, the entanglement entropy of a subsystem ${A}$ with length ${L_A}$ corresponds to the energy of the half-vortex pair ${S\sim \rho_s \log L_A}$, where ${\rho_s}$ is the total stiffness of the Goldstone modes. We also discuss special limits with more than one branch of Goldstone modes and comment on interaction effects., Comment: 16 pages, 4 figures

As proposed to describe putative continuous phase transitions between two ordered phases, the deconfined quantum critical point (DQCP) goes beyond the prevalent Landau-Ginzburg-Wilson (LGW) paradigm since its critical theory is not expressed in terms of the order parameters characterizing either state, but involves fractionalized degrees of freedom and an emergent symmetry. So far, great efforts have been spent on its equilibrium properties, but the nonequilibrium properties therein are largely unknown. Here we study the nonequilibrium dynamics of the DQCP via the imaginary-time evolution in the two-dimensional (2D) J-Q$_3$ model. We discover fascinating nonequilibrium scaling behaviors hinging on the process of fractionization and the dynamics of emergent symmetry associated with two length scales. Our findings not only constitute a new realm of nonequilibrium criticality in DQCP, but also offer a controllable knob by which to investigate the dynamics in strongly correlated systems., Comment: 19 pages, 14 figures

Charge-$4e$ superconductivity as a novel phase of matter remains elusive so far. Here we show that charge-$4e$ phase can arise as a vestigial order above the nematic superconducting transition temperature in time-reversal-invariant nematic superconductors. On the one hand, the nontrivial topological defect -- nematic vortex -- is energetically favored over the superconducting phase vortex when the nematic stiffness is less than the superfluid stiffness; consequently the charge-$4e$ phase emerges by proliferation of nematic vortices upon increasing temperatures. On the other hand, the Ginzburg-Landau theory of the nematic superconductors has two distinct decoupling channels to either charge-$4e$ orders or nematic orders; by analyzing the competition between the effective mass of the charge-$4e$ order and the cubic potential of the nematic order, we find a sizable regime where the charge-$4e$ order is favored. These two analysis consistently show that nematic superconductors can provide a promising route to realize charge-$4e$ phases, which may apply to candidate nematic superconductors such as PbTaSe$_2$ and twisted bilayer graphene., Comment: 4.5 pages + supplemental material, 3 figures

We show that a class of $\mathcal{PT}$ symmetric non-Hermitian Hamiltonians realizing the Yang-Lee edge singularity exhibits an entanglement transition in the long-time steady state evolved under the Hamiltonian. Such a transition is induced by a level crossing triggered by the critical point associated with the Yang-Lee singularity and hence is first-order in nature. At the transition, the entanglement entropy of the steady state jumps discontinuously from a volume-law to an area-law scaling. We exemplify this mechanism using a one-dimensional transverse field Ising model with additional imaginary fields, as well as the spin-1 Blume-Capel model and the three-state Potts model. We further make a connection to the forced-measurement induced entanglement transition in a Floquet non-unitary circuit subject to continuous measurements followed by post-selections. Our results demonstrate a new mechanism for entanglement transitions in non-Hermitian systems harboring a critical point., Comment: Updated to published version

In a recent paper by Lucas and Das Sarma [Physical Review B 97, 115449 (2018)], a solvable model of collective modes in 2D metals was considered in the hydrodynamic regime. In the current work, we generalize the hydrodynamic theory to 3D metals for which the calculation of sound modes in a strongly-coupled quantum Coulomb plasma can be made explicit. The specific theoretical question of interest is how the usual linearly dispersing hydrodynamic sound mode relates to the well-known gapped 3D plasmon collective mode in the presence of long-range Coulomb interaction. We show analytically that both the zero sound in the collisionless regime and the first sound in the hydrodynamic region become massive in 3D, acquiring a finite gap because of the long-range Coulomb interaction, while their damping rates become quadratic in momentum. We also discuss other types of long-range potential, where the dispersion of sound modes is modified accordingly. The general result is that the leading order hydrodynamic sound mode is always given by the leading-order plasmon frequency in the presence of long-range Coulomb interaction, but the next-to-leading-order dispersion corrections differ in hydrodynamic and colllisionless regimes., Comment: 11 pages, 1 figure

We study the time evolution of R\'enyi entropy in a system of two coupled Brownian SYK clusters evolving from an initial product state. The R\'enyi entropy of one cluster grows linearly and then saturates to the coarse grained entropy. This Page curve is obtained by two different methods, a path integral saddle point analysis and an operator dynamics analysis. Using the Brownian character of the dynamics, we derive a master equation which controls the operator dynamics and gives the Page curve for purity. Insight into the physics of this complicated master equation is provided by a complementary path integral method: replica diagonal and non-diagonal saddles are responsible for the linear growth and saturation of R\'enyi entropy, respectively., Comment: 33 pages

The concepts of operator size and computational complexity play important roles in the study of quantum chaos and holographic duality because they help characterize the structure of time-evolving Heisenberg operators. It is particularly important to understand how these microscopically defined measures of complexity are related to notions of complexity defined in terms of a dual holographic geometry, such as complexity-volume (CV) duality. Here we study partially entangled thermal states in the Sachdev-Ye-Kitaev (SYK) model and their dual description in terms of operators inserted in the interior of a black hole in Jackiw-Teitelboim (JT) gravity. We compare a microscopic definition of complexity in the SYK model known as K-complexity to calculations using CV duality in JT gravity and find that both quantities show an exponential-to-linear growth behavior. We also calculate the growth of operator size under time evolution and find connections between size and complexity. While the notion of operator size saturates at the scrambling time, our study suggests that complexity, which is well defined in both quantum systems and gravity theories, can serve as a useful measure of operator evolution at both early and late times., Comment: 23+5 pages, 6 figures, minor correction, version published in JHEP

Dynamical phase transition (DPT) characterizes the abrupt change of dynamical properties in nonequilibrium quantum many-body systems. It has been demonstrated that extra quantum fluctuating modes besides the conventional order parameter field can drastically change the properties of equilibrium phase transitions. However, the counterpart phenomena in DPTs have rarely been explored. Here, we study the DPT in the Dirac system after a sudden quench, and find that the fermion fluctuations can round a putative first-order DPT into a dynamical critical point, which is referred to as a fermion-induced dynamical critical point (FIDCP). It is also a nonthermal critical point, in which the universal short-time scaling behavior emerges despite the system goes through a first-order transition after thermalization. In the novel scenario of FIDCP, the quantum Yukawa coupling $g_q$ is indispensable for inducing the FIDCP albeit irrelevant in the infrared scale. We call these variables {\it indispensable irrelevant scaling variables}. Moreover, a dynamical tricritical point which separates the first-order DPT and the FIDCP is discovered by tuning this indispensable irrelevant scaling variable. We further mention possible experimental realizations., Comment: 6+4 pages, 4+4 figures

The existence or not of Landau poles is one of the oldest open questions in non-asymptotic quantum field theories. We investigate the Landau pole issue in two condensed matter systems whose long-wavelength physics is described by appropriate quantum field theories: the critical quantum magnet and Dirac fermions in graphene with long-range Coulomb interactions. The critical quantum magnet provides a classic example of a quantum phase transition, and it is well described by the $\phi^4$ theory. We find that the irrelevant but symmetry-allowed couplings, such as the $\phi^6$ potential, can significantly change the fate of the Landau pole in the $\phi^4$ theory. We obtain the coupled beta functions of a $\phi^4 + \phi^6$ potential at both small and large orders. Already from the 1-loop calculation, the Landau pole is replaced by an ultraviolet fixed point. A Lipatov analysis at large orders reveals that the inclusion of a $\phi^6$ term also has important repercussions for the high-order expansion of the beta functions. We also investigate the role of the Landau pole in 2+1 dimensional Dirac fermions with Coulomb interactions, e.g., graphene. Both the weak-coupling perturbation theory up to 2 loops and a low-order large-N calculation show the absence of a Landau pole. Furthermore, we calculate the asymptotic expansion coefficients of the beta function. We find that the asymptotic coefficient is bounded by that of a $\phi^4$ theory, so graphene is free from Landau poles if the $\phi^4$ theory does not manifest a Landau pole. We briefly discuss possible experiments that could potentially probe the existence of a Landau pole in these systems. Studying Landau poles in suitable condensed matter systems is of considerable fundamental importance since the relevant Landau pole energy scales in particle physics, whether it is quantum electrodynamics or Higgs physics, are completely unattainable., Comment: 17 pages, 5 figures

We investigate the $2k_F$ density-wave instability of non-Fermi liquid states by combining exact diagonalization with renormalization group analysis. At the half-filled zeroth Landau level, we study the fate of the composite Fermi liquid in the presence of the mass anisotropy and mixed Landau level form factors. These two experimentally accessible knobs trigger a phase transition towards a unidirectional charge-density-wave state with a wavevector equal to $2k_F$ of the composite Fermi liquid. Based on exact diagonalization, we identify such a transition by examining both the energy spectra and the static structure factor of charge density-density correlations. Moreover, the renormalization group analysis reveals that gauge fluctuations render the non-Fermi liquid state unstable against density-wave orders, consistent with numerical observations. Possible experimental probes of the density-wave instability are also discussed., Comment: 10 pages,8 figures

We study the prethermal dynamics of the Gross-Neveu-Yukawa quantum field theory, suddenly quenched in the vicinity of a quantum critical point. We find that the universal prethermal dynamics is controlled by two fixed points depending on the size of the quench. Besides the usual equilibrium chiral Ising fixed point for a shallow quench, a dynamical chiral Ising fixed point is identified for a deep quench. Intriguingly, the latter is a non-thermal fixed point without any equilibrium counterpart due to the participation of gapless fermionic fields. We also find that in the scaling regime controlled by the equilibrium fixed point, the initial slip exponent is rendered negative if there are enough flavors of fermions, thus providing a unique signature of fermionic prethermal dynamics. We then explore the temporal crossover between the universal scaling regimes governed by the two universality classes. Possible experimental realizations are also discussed., Comment: 4.2 pages + supplemental materials, 2 figures

Deconfined quantum criticality with emergent SO(5) symmetry in correlated systems remains elusive. Here, by performing numerically-exact state-of-the-art quantum Monte Carlo (QMC) simulations, we show convincing evidences of deconfined quantum critical points (DQCP) between antiferromagnetic and valence-bond-solid phases in the extended Hubbard model of fermions on the honeycomb lattice with large system sizes. We further demonstrate evidences of the SO(5) symmetry at the DQCP. It is important to note that the critical exponents obtained by finite-size scaling at the DQCP here are consistent with the rigourous conformal bounds. Consequently, we established a promising arena of DQCP with emergent SO(5) symmetry in interacting systems of fermions. Its possible experimental relevances in correlated systems of Dirac fermions will be discussed briefly., Comment: 5.6 pages + Supplemental Materials, 4 figures

Supersymmetry, a symmetry between fermions and bosons, provides a promising extension of the standard model but is still lack of experimental evidence. Recently, the interest in supersymmetry arises in the condensed matter community owing to its potential emergence at the continuous quantum phase transition. In this work, we demonstrate that 2+1D supersymmetry, relating massive Majorana and Ising fields, might emerge at the first-order quantum phase transition of the Ising magnetization by tuning a single parameter. Although the emergence of the SUSY is only allowed in a finite range of scales due to the existence of relevant masses, the scale range can be large when the masses before scaling are small. We show that the emergence of supersymmetry is accompanied by a topological phase transition for the Majorana field, where its non-zero mass changes the sign but keeps the magnitude. An experimental realization of this scenario is proposed using the surface state of a 3+1D time-reversal invariant topological superconductor with surface magnetic doping., Comment: Close to the published version. 16 pages and 5 figures

We study collective modes near the quantum critical point of a pair-density-wave (PDW) superconductor in 2+1 dimensions. The fate of gaps of various collective modes is investigated by functional renormalization. For incommensurate PDW superconductors, we show that the gapless Leggett mode, protected by the emergent $U(1)$ symmetry, can induce an exponentially small Higgs mass compared to the superconducting gap. Further, for commensurate PDW superconductors, we find an emergent mass hierarchy in the collective modes, i.e. the masses of Leggett boson, Higgs boson, and the superconducting gap can differ by several magnitudes in the infrared. This may shed light to a mechanism underlying the hierarchy problem in the Standard Model of particle physics., Comment: 8 pages, 5 figures

The shear viscosity is an important characterization of how a many-body system behaves like a fluid. We study the shear viscosity in a strongly interacting solvable model, consisting of coupled Sachdev-Ye-Kitaev (SYK) islands. As temperature is lowered, the model exhibits a crossover from an incoherent metal with local criticality to a marginal fermi liquid. We find that while the ratio of shear viscosity to entropy density in the marginal Fermi liquid regime satisfies a Kovtun-Son-Starinets (KSS) like bound, it can strongly violate the KSS bound in a robust temperature range of the incoherent metal regime, implying a nearly perfect fluidity of the coupled local critical SYK model. Furthermore, this model also provides the first translationally invariant example violating the KSS bound with known gauge-gravity correspondence., Comment: 10 pages, 2 figures; more details added as appendix; and minor corrections

Exotic physics often emerges around quantum criticality in metallic systems. Here we explore the nature of topological phase transitions between 3D double-Weyl semimetals and insulators (through annihilating double-Weyl nodes with opposite chiralities) in the presence of Coulomb interactions. From renormalization-group (RG) analysis, we find a non-Fermi-liquid quantum critical point (QCP) between the double-Weyl semimetals and insulators when artificially neglecting short-range interactions. However, it is shown that this non-Fermi-liquid QCP is actually unstable against nematic ordering when short-range interactions are correctly included in the RG analysis. In other words, the putative QCP between the semimetals and insulators is preempted by emergence of nematic phases when Coulomb interactions are present. We further discuss possible experimental relevance of the nematicity-preempted QCP to double-Weyl candidate materials HgCr2Se4 and SrSi2., Comment: 5.3 pages+supplemental materials, 4 figures

We study the coupled quantum Hall bilayers each at half-filled first excited Landau levels with varying the layer distance. Based on numerical exact diagonalization on torus, we identify two distinct phases separated by a critical layer distance $d_c$. From $d_c$ to infinite layer distance, the topological phase is smoothly connected to a direct tensor product of two Moore-Read states, while the interlayer coherence emerges at $d

Quantum chaos in many-body systems may be characterized by the Lyapunov exponent defined as the exponential growth rate of out-of-time-order correlators (OTOC). So far Lyaponov exponents around various quantum critical points (QCP) remain largely unexplored. Here, we investigate the Lyapunov exponent around QCPs of the Gross-Neveu (GN) model with $N$ flavors of Dirac fermions in (2+1) dimensions. Around the GN quantum phase transition between a Dirac semimetal and a gapped insulator breaking $Z_2$ symmetry (e.g., inversion symmetry of the honeycomb lattice), we find that the Lyaponov exponent $\lambda_L \approx 3.5 T/N$ at temperature $T$ and to the leading order of $1/N$ in the large-$N$ expansion. We also obtain the quantum scattering rate of an excitation with energy $\epsilon$, which is proportional to $\sqrt{\epsilon T}/N$ at low energy. We further discuss possible experimental relevances of the GN model in many-body systems., Comment: 7 pages, 7 figures + appendix

Many key features of the higher-dimensional Sachdev-Ye-Kitaev (SYK) model at {\it finite} $N$ remain unknown. Here we study the SYK chain consisting of $N$ ($N$$\ge$$2$) fermions per site with random interactions and hoppings between neighboring sites. In the limit of vanishing SYK interactions, from both supersymmetric field theory analysis and numerical calculations we find that the random hopping model exhibits Anderson localization at finite $N$, irrespective of the parity of $N$. Moreover, the localization length scales linearly with N, implying no Anderson localization \textit{only} at $N\!=\!\infty$. For finite SYK interaction $J$ , from the exact diagonalization we show that there is a dynamic phase transition between many-body localization and thermal diffusion as $J$ exceeds a critical value $J_c$. In addition, we find that the critical value $J_c$ decreases with the increase of $N$, qualitatively consistent with the analytical result of $J_c/t \!\propto\! \frac{1}{N^{5/2}\log N}$ derived from the weakly interacting limit., Comment: Published version

Tricriticality, as a sister of criticality, is a fundamental and absorbing issue in condensed matter physics. It has been verified that the bosonic Wilson-Fisher universality class can be changed by gapless fermionic modes at criticality. However, the counterpart phenomena at tricriticality have rarely been explored. In this paper, we study a model in which a tricritical Ising model is coupled to massless Dirac fermions. We find that the massless Dirac fermions result in the emergence of a new tricritical point, which we refer to as the chiral tricritical point (CTP), at the phase boundary between the Dirac semimetal and the charge-density-wave insulator. From functional renormalization group analysis of the effective action, we obtain the critical behaviors of the CTP, which are qualitatively distinct from both the tricritical Ising universality and the chiral Ising universality. We further extend the calculations of the chiral tricritical behaviors of Ising spins to the case of Heisenberg spins. The experimental relevance of the CTP in two-dimensional Dirac semimetals is also discussed., Comment: 4.3 pages + supplemental material, 2 figures, published version

We show that the quantum critical point (QCP) between a diffusive metal and ferromagnetic (or antiferromagnetic) phases in the SYK chain has a gravitational description corresponding to the double-trace deformation in an AdS$_2$ chain. Specifically, by studying a double-trace deformation of a $Z_2$ scalar in an AdS$_2$ chain where the $Z_2$ scalar is dual to the order parameter in the SYK chain, we find that the susceptibility and renormalization group equation describing the QCP in the SYK chain can be exactly reproduced in the holographic model. Our results suggest that the infrared geometry in the gravity theory dual to the diffusive metal of the SYK chain is also an AdS$_2$ chain. We further show that the transition in SYK model captures universal information about double-trace deformation in generic black holes with near horizon AdS$_2$ spacetime., Comment: 4.5 pages + supplemental material, 1 figure, published version

We investigate novel topological magnon band crossings of pyrochlore antiferromagnets with all-in-all-out (AIAO) magnetic order. By general symmetry analysis and spin-wave theory, we show that pyrochlore materials with AIAO orders can host Weyl magnons under external magnetic fields or uniaxial strains. Under a small magnetic field, the magnon bands of the pyrochlore with AIAO background can feature two opposite-charged Weyl points, which is the minimal number of Weyl points realizable in quantum materials and has not be experimentally observed so far. We further show that breathing pyrochlores with AIAO orders can exhibit Weyl magnons upon uniaxial strains. These findings apply to any pyrochlore material supporting AIAO orders, irrespective of the forms of interactions. Specifically, we show that the Weyl magnons are robust against direct (positive) Dzyaloshinskii-Moriya interactions. Because of the ubiquitous AIAO orders in pyrochlore magnets including R$_2$Ir$_2$O$_7$, and experimentally achievable external strain and magnetic field, our predictions provide promising arena to witness the Weyl magnons in quantum magnets., Comment: 5 pages+supplemental materials, 6 figures

Many aspects of many-body localization (MBL) transitions remain elusive so far. Here, we propose a higher-dimensional generalization of the Sachdev-Ye-Kitaev (SYK) model and show that it exhibits a MBL transition. The model on a bipartite lattice has $N$ Majorana fermions with SYK interactions on each site of the $A$ sublattice and $M$ free Majorana fermions on each site the of $B$ sublattice, where $N$ and $M$ are large and finite. For $r$$\equiv$$M/N\!<\!r_c$=1, it describes a diffusive metal exhibiting maximal chaos. Remarkably, its diffusive constant $D$ vanishes [$D$$\propto$$ (r_c-r)^{1/2}$] as $r$$\rightarrow$$r_c$, implying a dynamical transition to a MBL phase. It is further supported by numerical calculations of level statistics which changes from Wigner-Dyson ($r$$<$$r_c$) to Poisson ($r$$>$$r_c$) distributions. Note that no subdiffusive phase intervenes between diffusive and MBL phases. Moreover, the critical exponent $\nu$=0, violating the Harris criterion. Our higher-dimensional SYK model may provide a promising arena to explore exotic MBL transitions., Comment: published version in PRL

We study interaction effects, including both long-ranged Coulomb and short-range interactions, in three-dimensional topological triple-Weyl semimetals whose triple-Weyl points are protected by crystal symmetries. By performing Wilsonian renormalization group analysis of the low-energy effective field theory of the minimal model with triple-Weyl nodes, we find that the fixed point of noninteracting triple-Weyl fermions is unstable in the presence of Coulomb interactions and flows to a nontrivial stable fixed point representing marginal Fermi liquids with anisotropic screening effects. We further discuss relevant unusual physical consequences due to the novel behavior of correlation effects in this system., Comment: 4.7 pages+appendix, 4 figures. Update references

In this paper we investigate the nature of quantum phase transitions between two-dimensional Dirac semimetals and $Z_3$-ordered phases (e.g. Kekule valence-bond solid), where cubic terms of the order parameter are allowed in the quantum Landau-Ginzberg theory and the transitions are putatively first-order. From large-$N$ renormalization group (RG) analysis, we find that fermion-induced quantum critical points (FIQCPs) [Z.-X. Li et al., Nature Communications 8, 314 (2017)] occur when $N$ (the number of flavors of four-component Dirac fermions) is larger than a critical value $N_c$. Remarkably, from the knowledge of spacetime supersymmetry, we obtain an exact lower bound for $N_c$, i.e., $N_c>1/2$. (Here the "1/2" flavor of four-component Dirac fermions is equivalent to one flavor of four-component Majorana fermions). Moreover, we show that the emergence of two length scales is a typical phenomenon of FIQCPs and obtain two different critical exponents, i.e., $\nu$$\neq$$\nu'$, by large-$N$ RG calculations. We further give a brief discussion on possible experimental realizations of FIQCPs., Comment: 7.6 pages, 6 figures, published version

Fermion-induced quantum critical points (FIQCPs) were recently discovered at the putatively first-order transitions between two-dimensional (2D) Dirac semimetals and the Kekule valence bond solids on the honeycomb lattice by sign-free quantum Monte Carlo simulations [Nature Communications 8, 314, (2017)]. Here, we investigate possible FIQCP in 3D topological Weyl semimetals at a $Z_3$ symmetry-breaking transition that is putatively first-order according to the Landau criterion. We construct a lattice model featuring 3D double-Weyl fermions (monopole charges $\pm$2) and we show that $Z_3$ nodal-nematic transitions occur under finite Hubbard interaction. Furthermore, using renormalization-group analysis, we identify such a transition as a genuine FIQCP where the cubic terms are irrelevant and an enlarged U(1) symmetry emerges at low energy. We further discuss quantum critical behaviors and experimental signatures of such FIQCPs in 3D double-Weyl semimetals., Comment: 4.5 pages + appendixes, 3 figures, added a lattice model and the mean field theory, added new figures, updated references, corrected typos, the published version

Supersymmetric (SUSY) gauge theories such as the Minimal Supersymmetric Standard Model play a fundamental role in modern particle physics, but have not been verified so far in nature. Here, we show that a SUSY gauge theory with dynamical gauge bosons and fermionic gauginos emerges naturally at the pair-density-wave (PDW) quantum phase transition on the surface of a correlated topological insulator (TI) hosting three Dirac cones, such as the topological Kondo insulator SmB$_6$. At the quantum tricritical point between the surface Dirac semimetal and nematic PDW phases, three massless bosonic Cooper pair fields emerge as the superpartners of three massless surface Dirac fermions. The resulting low-energy effective theory is the supersymmetric XYZ model, which is dual by mirror symmetry to $\mathcal{N}=2$ supersymmetric quantum electrodynamics (SQED) in 2+1 dimensions, providing a first example of emergent supersymmetric gauge theory in condensed matter systems. Supersymmetry allows us to determine exactly certain critical exponents and the optical conductivity of the surface states at the strongly coupled tricritical point, which may be measured in future experiments., Comment: Published version in Phys. Rev. Lett; More discussions about broader impact of our results to general SUSY theories are added

A unified theory of quantum critical points beyond the conventional Landau-Ginzburg-Wilson paradigm remains unknown. According to Landau cubic criterion, phase transitions should be first-order when cubic terms of order parameters are allowed by symmetry in the Landau-Ginzburg free energy. Here, from renormalization group (RG) analysis we show that second-order quantum phase transitions can occur at such putatively first-order transitions in interacting two-dimensional Dirac semimetals. As such type of Landau-forbidden quantum critical points are induced by gapless fermions, we call them fermion-induced quantum critical points (FIQCP). We further introduce a microscopic model of SU(N) fermions on the honeycomb lattice featuring a transition between Dirac semimetals and Kekule valence bond solids. Remarkably, our large-scale sign-problem-free Majorana quantum Monte Carlo simulations show convincing evidences of a FIQCP for N=2,3,4,5,6, consistent with the RG analysis. We finally discuss possible experimental realizations of the FIQCP in graphene and graphene-like materials., Comment: Accepted in Nature Communications. Initial submission to a different journal on Jan. 5th, 2016. The supersymmetry argument is added

We study the fate of double-Weyl fermions in three-dimensional systems in the presence of long-range Coulomb interactions. By employing the momentum-shell renormalization group approach, we find that the fixed point of noninteracting double-Weyl fermions is unstable against Coulomb interactions and flows to a nontrivial stable fixed point with anisotropic screening effect. Moreover, experimentally measurable quantities such as specific heat obtain unusual logarithmic corrections. We also discuss implications of our results to three-dimensional materials HgCr2Se4 and SrSi2, candidate materials of hosting double-Weyl fermions., Comment: 11.1 pages, 4 figures, published version in Physical Review B

Supersymmetry (SUSY) interchanges bosons and fermions but no direct evidences of it have been revealed in nature yet. In this letter, we observe that fluctuating pair density waves (PDW) consist of two complex order parameters which can be superpartners of the unavoidably-doubled Weyl fermions in three-dimensional lattice models. We construct explicit fermionic lattice models featuring 3D Weyl fermions and show that PDW is the leading instability via a continuous phase transition as short-range interactions exceed a critical value. Using renormalization group, we theoretically show that N=2 space-time SUSY emerges at the continuous PDW transitions in 3D Weyl semimetals, which we believe is the first realization of emergent (3+1)D space-time SUSY in microscopic lattice models. We further discuss possible routes to realize such lattice models and experimental signatures of emergent SUSY at the PDW criticality., Comment: 4.9 pages, 4 figures, published version in Physical Review Letters, Editors' Suggestion in PRL