arXiv subjects

Erhai Zhao

Publications and source records attributed to Erhai Zhao.

At least 19 recordsLinked to original sources

arXiv2026

Complexity transition in the Dicke model of light-matter interaction

Tuning the coupling strength $g$ of an interacting quantum system may drive a sudden change in its ground-state or thermal properties. To identify and grasp non-analytical, or even discontinuous, transitions in far-from-equilibrium dynamics proves more challenging. Recently Krylov complexity $C_K$ has offered fresh insights about operator growth, thermalization, and chaos in quantum dynamics. Yet it remains unclear if, and how, changing $g$ can trigger a sharp transition in the complexity measures. Here we present evidence for such a transition by mapping out the complexity phase diagram of the paradigmatic Dicke model describing two-level atoms coupled to a cavity photon mode. Two qualitatively different regimes of dynamics are identified and characterized. At the transition, the slope of $C_K$ changes suddenly to coincide with a jump in the Krylov entropy. We elucidate the nature of the regime change from the wave packet dynamics in Krylov space, where a particle is confined by a roughly linear potential but hops as if it lives in a Rindler reference frame. The competition between confinement, which leads to bouncing, and deconfinement by Rindler hopping, which leads to the destruction of wave packet analogous to gravitational spaghettification, is sensitive to the disorder in Lanczos coefficients. The framework outlined here can be applied to other quantum many-body systems.

cond-mat.quant-gas↗

arXiv2026

Giant bubbles of Fisher zeros in the quantum XY chain

We demonstrate an alternative approach based on complex-valued inverse temperature and partition function to probe quantum phases of matter with nontrivial spectra and dynamics. It leverages thermofield dynamics (TFD) to quantitatively characterize quantum and thermal fluctuations, and exploit the correspondence between low-energy excitations and Fisher zeros. Using the quantum XY chain in an external field as a testbed, we show that the oscillatory gap behavior manifests as oscillations in the long-time dynamics of the TFD spectral form factor. We also identify giant bubbles, i.e. large-scale closed lines, of Fisher-zeros near the gapless XX limit. They provide a characteristic energy scale that seems to contradict the predictions of the low energy theory of a featureless Luttinger liquid. We identify this energy scale and relate the motion of these giant bubbles with varying external field to the transfer of spectral weight from high to low energies. The deep connection between Fisher zeros, dynamics, and excitations opens up promising avenues for understanding the unconventional gap behaviors in strongly correlated many-body systems.

cond-mat.str-el↗

arXiv2026

Double-exchange ferromagnetism of fermionic atoms in a $p$-orbital hexagonal lattice

A large class of correlated quantum materials feature strong Hund's coupling. Yet cold-atom quantum simulators have so far focused primarily on single-orbital Fermi-Hubbard systems near a Mott insulator. Here we show that repulsively interacting fermions loaded into the $p$-bands of a hexagonal lattice offer a unique platform to study the interplay of "Hundness" and "Mottness." Our theory predicts that the orbital degrees of freedom, despite geometric frustration, produce a rich phase diagram featuring a competing itinerant ferromagnetic (FM) metal and a spin-1 antiferromagnetic (AFM) insulator, with a surprising first-order transition between them controlled by density near half-filling. Ferromagnetism emerges at low fillings from the flat band and persists to stronger interactions and higher fillings via a double-exchange mechanism, where spins align to avoid Hund-rule penalties at the expense of Dirac-fermion kinetic energy. We further argue that the paramagnetic regime is a correlated "Hund metal." $p$-orbital Fermi gases thus provide an ideal experimental setting to investigate competing exchange mechanisms in multi-orbital systems with coexisting localized and itinerant spins.

cond-mat.quant-gas↗

arXiv2025

Detecting Many-Body Scars from Fisher Zeros

The far-from-equilibrium dynamics of certain interacting quantum systems still defy precise understanding. One example is the so-called quantum many-body scars (QMBSs), where a set of energy eigenstates evade thermalization to give rise to long-lived oscillations. Despite the success of viewing scars from the perspectives of symmetry, commutant algebra, and quasiparticles, it remains a challenge to elucidate the mechanism underlying all QMBS and to distinguish them from other forms of ergodicity breaking. In this work, we introduce an alternative route to detect and diagnose QMBS based on Fisher zeros, i.e., the patterns of zeros of the analytically continued partition function $Z$ on the complex $β$ (inverse temperature) plane. For systems with scars, a continuous line of Fisher zeros will appear off the imaginary $β$ axis and extend upward, separating the $β$ plane into regions with distinctive thermalization behaviors. This conjecture is motivated from interpreting the complex $Z$ as the return amplitude of the thermofield double state, and it is validated by analyzing two models with QMBS, the $\bar{P}X\bar{P}$ model and the Ising chain in external fields. These models also illustrate the key difference between QMBS and strong ergodicity breaking including their distinctive renormalization group flows on the complex $β$ plane. This ``statistical mechanics" approach places QMBS within the same framework of thermal and dynamical phase transitions. It has the advantage of spotting scars without exhaustively examining each individual quantum state.

cond-mat.str-el↗

arXiv2025

Topological Feature of Real-time Fisher Zeros

There are numerous methods to characterize topology and its boundary zero modes, yet their statistical mechanical properties have not received as much attention as other approaches. Here, we investigate the Fisher zeros and thermofield dynamics of topological models, revealing that boundary zero modes can be described by an overlooked real-time Fisher zero pairing effect. This effect is validated in the Su-Schrieffer-Heeger model and the Kitaev chain model, with the latter exhibiting a Fisher zero braiding picture. Topological zero modes exhibit robustness even when non-Hermiticity is introduced into the system and display characteristics of imaginary-time crystals when the energy eigenvalues are complex. We further examine the real-time Fisher zeros of the one-dimensional transverse field Ising model, which maps to the Kitaev chain. We present a fractal picture of the Fisher zeros, illustrating how interactions eliminate topology. The mechanism of zero-pairing provides a natural statistical mechanical approach to understanding the connection between topology and many-body physics.

cond-mat.str-el↗

arXiv2025

From Complexification to Self-Similarity: New Aspects of Quantum Criticality

Quantum phase transitions are a fascinating area of condensed matter physics. The extension through complexification not only broadens the scope of this field but also offers a new framework for understanding criticality and its statistical implications. This mini review provides a concise overview of recent developments in complexification, primarily covering finite temperature and equilibrium quantum phase transitions, as well as their connection with dynamical quantum phase transitions and non-Hermitian physics, with a particular focus on the significance of Fisher zeros. Starting from the newly discovered self-similarity phenomenon associated with complex partition functions, we further discuss research on self-similar systems briefly. Finally, we offer a perspective on these aspects.

cond-mat.str-el↗

arXiv2025

Exact Fisher zeros and thermofield dynamics across a quantum critical point

By setting the inverse temperature $β$ loose to occupy the complex plane, Fisher showed that the zeros of the complex partition function $Z$, if approaching the real $β$ axis, reveal a thermodynamic phase transition. More recently, Fisher zeros were used to mark the dynamical phase transition in quench dynamics. It remains unclear, however, how Fisher zeros can be employed to better understand quantum phase transitions or the non-unitary dynamics of open quantum systems. Here we answer this question by a comprehensive analysis of the analytically continued one-dimensional transverse field Ising model. We exhaust all the Fisher zeros to show that in the thermodynamic limit they congregate into a remarkably simple pattern in the form of continuous open or closed lines. These Fisher lines evolve smoothly as the coupling constant is tuned, and a qualitative change identifies the quantum critical point. By exploiting the connection between $Z$ and the thermofield double states, we obtain analytical expressions for the short- and long-time dynamics of the survival amplitude, including its scaling behavior at the quantum critical point. We point out $Z$ can be realized and probed in monitored quantum circuits. The exact analytical results are corroborated by the numerical tensor renormalization group. We further show that similar patterns of Fisher zeros also emerge in other spin models. Therefore, the approach outlined may serve as a powerful tool for interacting quantum systems.

cond-mat.str-el↗

arXiv2024

Pairing from repulsion in a two-dimensional Fermi gas with soft-core interactions

We investigate a model many-body system of spinless Fermi gas in two dimensions, where the bare two-body interaction is repulsive and takes the form of a soft-core disk potential. We obtain the zero temperature phase diagram of this model by numerical functional renormalization group (FRG), which retains the effective interaction vertices in all channels to provide a detailed picture of how Cooper pairing emerges under the renormalization flow. The repulsion drives the system to a series of superfluid states with higher angular momentum paring, for example in the $f$- and $h$-wave channels instead of the $p$-wave channel. This is in sharp contrast to the original Kohn-Luttinger mechanism where pairing of very large angular momenta and exponentially small transition temperature was predicted. We trace the stabilization and enhancement of $f$- and $h$-wave pairing back to the momentum dependence of the bare interaction. A perturbative calculation is carried out to show that while the second order Kohn-Luttinger diagrams provide a qualitative understanding of the onsets of the various superfluid phases, they are unable to accurately capture the phase boundaries predicted by FRG. Our findings suggest that tuning the shape of the interaction potential offers a promising route to achieve stronger ``pairing glue" and to realize nontrivial superfluid phases in repulsive Fermi gases beyond the scope of the original Kohn-Luttinger analysis.

cond-mat.quant-gas↗

arXiv2023

Unravelling the edge spectra of non-Hermitian Chern insulators

Non-Hermitian Chern insulators differ from their Hermitian cousins in one key aspect: their edge spectra are incredibly rich and confounding. For example, even in the simple case where the bulk spectrum consists of two bands with Chern number $\pm 1$, the edge spectrum in the slab geometry may have one or two edge states on both edges, or only at one of the edges, depending on the model parameters. This blatant violation of the familiar bulk-edge correspondence casts doubt on whether the bulk Chern number can still be a useful topological invariant, and demands a working theory that can predict and explain the myriad of edge spectra from the bulk Hamiltonian to restore the bulk-edge correspondence. We outline how such a theory can be set up to yield a thorough understanding of the edge phase diagram based on the notion of the generalized Brillouin zone (GBZ) and the asymptotic properties of block Toeplitz matrices. The procedure is illustrated by solving and comparing three non-Hermitian generalizations of the Qi-Wu-Zhang model, a canonical example of two-band Chern insulators. We find that, surprisingly, in many cases the phase boundaries and the number and location of the edge states can be obtained analytically. Our analysis also reveals a non-Hermitian semimetal phase whose energy-momentum spectrum forms a continuous membrane with the edge modes transversing the hole, or genus, of the membrane. Subtleties in defining the Chern number over GBZ, which in general is not a smooth manifold and may have singularities, are demonstrated using examples. The approach presented here can be generalized to more complicated models of non-Hermitian insulators or semimetals in two or three dimensions.

cond-mat.mes-hall↗

arXiv2022

Dynamical signatures of point-gap Weyl semimetal

We demonstrate a few unique dynamical properties of point-gap Weyl semimetal, an intrinsic non-Hermitian topological phase in three dimensions. We consider a concrete model where a pair of Weyl points reside on the imaginary axis of the complex energy plane, opening up a point gap characterized by a topological invariant, the three-winding number $W_3$. This gives rise to surface spectra and dynamical responses that differ fundamentally from those in Hermitian Weyl semimetals. First, we predict a time-dependent current flow along the magnetic field in the absence of an electric field, in sharp contrast to the current driven by the chiral anomaly, which requires both electric and magnetic fields. Second, we reveal a novel type of boundary-skin mode in the wire geometry which becomes localized at two corners of the wire cross section. We explain its origin and show its experimental signatures in wave-packet dynamics.

cond-mat.mes-hall↗

arXiv2022

Rise and fall of plaquette order in Shastry-Sutherland magnet revealed by pseudo-fermion functional renormalization group

The Shastry-Sutherland model as a canonical example of frustrated magnetism has been extensively studied. The conventional wisdom has been that the transition from the plaquette valence bond order to the Neel order is direct and potentially realizes a deconfined quantum critical point beyond the Ginzburg-Landau paradigm. This scenario however was challenged recently by improved numerics from density matrix renormalization group which offers evidence for a narrow gapless spin liquid between the two phases. Prompted by this controversy and to shed light on this intricate parameter regime from a fresh perspective, we report high-resolution functional renormalization group analysis of the generalized Shastry-Sutherland model. The flows of over 50 million running couplings provide a detailed picture for the evolution of spin correlations as the frequency/energy scale is dialed from the ultraviolet to the infrared to yield the zero temperature phase diagram. The singlet dimer phase emerges as a fixed point, the Neel order is characterized by divergence in the vertex function, while the transition into and out of the plaquette order is accompanied by pronounced peaks in the plaquette susceptibility. The plaquette order is suppressed before the onset of the Neel order, lending evidence for a finite spin liquid region for $J_1/J_2\in (0.77,0.82)$, where the flow is continuous without any indication of divergence.

cond-mat.str-el↗

arXiv2022

Learning a compass spin model with neural network quantum states

Neural network quantum states provide a novel representation of the many-body states of interacting quantum systems and open up a promising route to solve frustrated quantum spin models that evade other numerical approaches. Yet its capacity to describe complex magnetic orders with large unit cells has not been demonstrated, and its performance in a rugged energy landscape has been questioned. Here we apply restricted Boltzmann machines and stochastic gradient descent to seek the ground states of a compass spin model on the honeycomb lattice, which unifies the Kitaev model, Ising model and the quantum 120$^\circ$ model with a single tuning parameter. We report calculation results on the variational energy, order parameters and correlation functions. The phase diagram obtained is in good agreement with the predictions of tensor network ansatz, demonstrating the capacity of restricted Boltzmann machines in learning the ground states of frustrated quantum spin Hamiltonians. The limitations of the calculation are discussed. A few strategies are outlined to address some of the challenges in machine learning frustrated quantum magnets.

cond-mat.str-el↗

arXiv2021

Illuminating the bulk-boundary correspondence of a non-Hermitian stub lattice with Majorana stars

Topological characterization of non-Hermitian band structures demands more than a straightforward generalization of the Hermitian cases. Even for one-dimensional tight-binding models with nonreciprocal hopping, the appearance of point gaps and the skin effect leads to the breakdown of the usual bulk-boundary correspondence. Luckily, the correspondence can be resurrected by introducing a winding number for the generalized Brillouin zone for systems with even number of bands and chiral symmetry. Here, we analyze the topological phases of a nonreciprocal hopping model on the stub lattice, where one of the three bands remains flat. Due to the lack of chiral symmetry, the biorthogonal Zak phase is no longer quantized, invalidating the winding number as a topological index. Instead, we show that a $Z_2$ invariant can be defined from Majorana's stellar representation of the eigenstates on the Bloch sphere. The parity of the total azimuthal winding of the entire Majorana constellation correctly predicts the appearance of edge states between the bulk gaps. We further show that the system is not a square-root topological insulator, despite the fact that its parent Hamiltonian can be block diagonalized and related to a sawtooth lattice model. The analysis presented here may be generalized to understand other non-Hermitian systems with multiple bands.

cond-mat.mes-hall↗

arXiv2021

Knots and Non-Hermitian Bloch Bands

Knots have a twisted history in quantum physics. They were abandoned as failed models of atoms. Only much later was the connection between knot invariants and Wilson loops in topological quantum field theory discovered. Here we show that knots tied by the eigenenergy strings provide a complete topological classification of one-dimensional non-Hermitian (NH) Hamiltonians with separable bands. A $\mathbb{Z}_2$ knot invariant, the global biorthogonal Berry phase $Q$ as the sum of the Wilson loop eigenphases, is proved to be equal to the permutation parity of the NH bands. We show the transition between two phases characterized by distinct knots occur through exceptional points and come in two types. We further develop an algorithm to construct the corresponding tight-binding NH Hamiltonian for any desired knot, and propose a scheme to probe the knot structure via quantum quench. The theory and algorithm are demonstrated by model Hamiltonians that feature for example the Hopf link, the trefoil knot, the figure-8 knot and the Whitehead link.

cond-mat.mes-hall↗

arXiv2020

Tuning the topology of $p$-wave superconductivity in an analytically solvable two-band model

We introduce and solve a two-band model of spinless fermions with $p_x$-wave pairing on a square lattice. The model reduces to the well-known extended Harper-Hofstadter model with half-flux quanta per plaquette and weakly coupled Kitaev chains in two respective limits. We show that its phase diagram contains a topologically nontrivial weak pairing phase as well as a trivial strong pairing phase as the ratio of the pairing amplitude and hopping is tuned. Introducing periodic driving to the model, we observe a cascade of Floquet phases with well defined quasienergy gaps and featuring chiral Majorana edge modes at the zero- or $π$-gap, or both. Dynamical topological invariants are obtained to characterize each phase and to explain the emergence of edge modes in the anomalous phase where all the quasienergy bands have zero Chern number. Analytical solution is achieved by exploiting a generalized mirror symmetry of the model, so that the effective Hamiltonian is decomposed into that of spin-$1/2$ in magnetic field, and the loop unitary operator becomes spin rotations. We further show the dynamical invariants manifest as the Hopf linking numbers.

cond-mat.supr-con↗

arXiv2020

Quench dynamics of Hopf insulators

Hopf insulators are exotic topological states of matter outside the standard ten-fold way classification based on discrete symmetries. Its topology is captured by an integer invariant that describes the linking structures of the Hamiltonian in the three-dimensional momentum space. In this paper, we investigate the quantum dynamics of Hopf insulators across a sudden quench and show that the quench dynamics is characterized by a $\mathbb{Z}_2$ invariant $ν$ which reveals a rich interplay between quantum quench and static band topology. We construct the $\mathbb{Z}_2$ topological invariant using the loop unitary operator, and prove that $ν$ relates the pre- and post-quench Hopf invariants through $ν=(\mathcal{L}-\mathcal{L}_0)\bmod 2$. The $\mathbb{Z}_2$ nature of the dynamical invariant is in sharp contrast to the $\mathbb{Z}$ invariant for the quench dynamics of Chern insulators in two dimensions. The non-trivial dynamical topology is further attributed to the emergence of $π$-defects in the phase band of the loop unitary. These $π$-defects are generally closed curves in the momentum-time space, for example, as nodal rings carrying Hopf charge.

cond-mat.quant-gas↗

arXiv2020

Topological Invariants for Quantum Quench Dynamics from Unitary Evolution

Recent experiments began to explore the topological properties of quench dynamics, i.e. the time evolution following a sudden change in the Hamiltonian, via tomography of quantum gases in optical lattices. In contrast to the well established theory for static band insulators or periodically driven systems, at present it is not clear whether, and how, topological invariants can be defined for a general quench of band insulators. Previous work solved a special case of this problem beautifully using Hopf mapping of two-band Hamiltonians in two dimensions. But it only works for topologically trivial initial state and is hard to generalize to multiband systems or other dimensions. Here we introduce the concept of loop unitary constructed from the unitary time-evolution operator, and show its homotopy invariant fully characterizes the dynamical topology. For two-band systems in two dimensions, we prove that the invariant is precisely equal to the change in the Chern number across the quench regardless of the initial state. We further show that the nontrivial dynamical topology manifests as hedgehog defects in the loop unitary, and also as winding and linking of its eigenvectors along a curve where dynamical quantum phase transition occurs. This opens up a systematic route to classify and characterize quantum quench dynamics.

cond-mat.mes-hall↗

arXiv2020

$f$-wave superfluidity from repulsive interaction in Rydberg-dressed Fermi gas

Interacting Fermi gas provides an ideal model system to understand unconventional pairing and intertwined orders relevant to a large class of quantum materials. Rydberg-dressed Fermi gas is a recent experimental system where the sign, strength, and range of the interaction can be controlled. The interaction in momentum space has a negative minimum at $q_c$ inversely proportional to the characteristic length-scale in real space, the soft-core radius $r_c$. We show theoretically that single-component (spinless) Rydberg-dressed Fermi gas in two dimensions has a rich phase diagram with novel superfluid and density wave orders due to the interplay of the Fermi momentum $p_F$, interaction range $r_c$, and interaction strength $u_0$. For repulsive bare interactions $u_0>0$, the dominant instability is $f$-wave superfluid for $p_Fr_c\lesssim 2$, and density wave for $p_Fr_c\gtrsim 4$. The $f$-wave pairing in this repulsive Fermi gas is reminiscent of the conventional Kohn-Luttinger mechanism, but has a much higher $T_c$. For attractive bare interactions $u_0<0$, the leading instability is $p$-wave pairing. The phase diagram is obtained from functional renormalization group that treats all competing many-body instabilities in the particle-particle and particle-hole channels on equal footing.

cond-mat.quant-gas↗