arXiv subjects

Cui-Xian Guo

Publications and source records attributed to Cui-Xian Guo.

At least 19 recordsLinked to original sources

arXiv2026

Decoding Equilibrium and Dynamical Criticality in the 2D Topological Order

Analytically connecting equilibrium criticality and dynamical quantum phase transitions (DQPTs) under complex driving fields remains a significant challenge, primarily due to the combinatorial complexity of non-local long-range entanglement. Here, we decode this connection in the 2D strongly interacting Wen-plaquette model. By mapping its anyonic excitations to 1D effective dissipative channels, we reveal that microscopic single-particle fidelity zeros exactly reconstruct the macroscopic equilibrium topological phase boundaries. Beyond equilibrium, we demonstrate that during non-unitary quench dynamics, these very same static singularities enforce a momentumspace exclusion against dynamical Fisher zeros. Furthermore, a newly identified dissipation-phase racing mechanism prematurely depletes the decaying mode, suppressing DQPTs and generating topologically trivial steady states. Our results establish exact microscopic static singularities as an analytical decoder for macroscopic non-unitary topological dynamics involving discrete symmetry breaking.

cond-mat.str-el↗

arXiv2026

A Unified Framework for the Non-Hermitian Localization: Boundary-Insensitive Modes and Electric-Magnetic Analogy

The non-Hermitian skin effect is fundamentally characterized by its sensitivity to boundary conditions, reflected in changes to the energy spectrum and boundary-localized eigenstates. Here, we demonstrate that a spatially inhomogeneous imaginary scalar potential field induces a skin effect that is insensitive to boundary conditions. Both the spectrum and eigenstate distribution remain invariant, a behavior not captured by existing theories. We attribute this anomaly to translational symmetry breaking induced by spatially varying imaginary potentials in finite systems. We further formulate a theory that universally predicts localization in single-particle non-Hermitian systems. This framework classifies skin effects into two fundamental types: electric, driven by imaginary scalar potentials, and magnetic, driven by imaginary vector potentials, and reveals a phase transition between them, where eigenstates become fully delocalized. Our work provides a unified theory for non-Hermitian localization, allowing full control over skin modes via potential engineering in various platforms like photonic crystals and cold-atom systems.

cond-mat.mes-hall↗

arXiv2026

Tailoring Corner States and Exceptional Points in Altermagnets

Altermagnets (AMs) exhibit vanishing net magnetization but strong momentum-dependent spin splitting enforced by crystal symmetry. Here, we explore the non-Hermitian effects in dissipative two-dimensional AMs. We show that symmetry-compliant dissipation naturally induces an imaginary staggered exchange field, driving a NH topological phase transition absent in conventional antiferromagnets. In the topologically nontrivial phase, hybrid skin-topological modes driven by altermagnetic d-wave anisotropy emerge, as captured by the chiral skin effect framework. In the gapless phase, we elucidate the creation and annihilation dynamics of exceptional points. Crucially, we analytically prove via the transfer matrix method that corner states are deterministically controlled by the boundary sublattice termination. Owing to the symmetry constraints and the robustness of chiral states, these findings hold universally across all topological AMs. A general framework is established for controlling topological corner states, offering a new strategy for designing magnetic materials with tailored non-Hermitian properties.

cond-mat.mes-hall↗

arXiv2025

Tuning Topological States by Dissipation

The bulk-boundary correspondence plays a crucial role in topological quantum systems, however,this principle is broken in non-Hermitian systems. The breakdown of the bulk-boundary correspondence indicates that the global phase diagrams under open boundary conditions are significantly different from those under periodic boundary conditions. In this paper, we investigate how the bulk-boundary correspondence breaks down by gradually tearing the system. We find that by tuning the strength of gain and loss domain wall, in the thermodynamic limit, the global phase diagrams of the topological system become the hybrids of those under periodic and open boundary conditions. Moreover, during the breakdown of the bulk-boundary correspondence, several phase transitions occur. This situation is quite different from earlier work, where the breakdown of the bulk-boundary correspondence in the thermodynamic limit occurred suddenly due to infinitesimal boundary hopping amplitudes. To support our conclusions, we provide both analytical and numerical calculations. These results help researchers better understand non-Hermitian topological systems.

quant-ph↗

arXiv2024

Scale-tailored localization and its observation in non-Hermitian electrical circuits

Anderson localization and non-Hermitian skin effect are two paradigmatic wave localization phenomena, resulting from wave interference and the intrinsic non-Hermitian point gap, respectively. In this study, we unveil a novel localization phenomenon associated with long-range asymmetric coupling, termed scale-tailored localization, where the number of induced localized modes and their localization lengths scale exclusively with the coupling range. We show that the long-range coupling fundamentally reshapes the energy spectra and eigenstates by creating multiple connected paths on the lattice. Furthermore, we present experimental observations of scale-tailored localization in non-Hermitian electrical circuits utilizing adjustable voltage followers and switches. The circuit admittance spectra possess separate point-shaped and loop-shaped components in the complex energy plane, corresponding respectively to skin modes and scale-tailored localized states. Our findings not only expand and deepen the understanding of peculiar effects induced by non-Hermiticity but also offer a feasible experimental platform for exploring and controlling wave localizations.

cond-mat.mes-hall↗

arXiv2023

Accumulation of scale-free localized states induced by local non-Hermiticity

The bulk states of Hermitian systems are believed insensitive to local Hermitian impurities or perturbations except for a few impurity-induced bound states. Thus, it is important to ask whether \textit{local} non-Hermiticity can cause drastic changes to the original Hermitian systems. Here we address this issue affirmatively and present exact solutions for the double chain model with local non-Hermitian terms possessing parity-time ($\mathcal{PT}$) symmetry. Induced by the non-Hermiticity, the system undergoes a sequence of $\mathcal{PT}$-symmetry breakings, after which the eigenenergies appear in complex conjugate pairs. The associated extended bulk states then become scale-free localized and unidirectionally accumulated around the impurity. There exist mobility edges separating the residual extended states until a full scale-free localization of all eigenstates. Further increasing the non-Hermitity counter-intuitively brings the system to a $\mathcal{PT}$-restoration regime with fully real spectra except for a pair of complex bound states. We demonstrate that the local non-Hermiticity generated scale-free localization is a general phenomenon and can even survive the quasiperiodic disorder. Our results indicate that the bulk properties of the original Hermitian system can be globally reshaped by local non-Hermiticity.

quant-ph↗

arXiv2023

Exceptional Non-Abelian Topology in Multiband Non-Hermitian Systems

Defective spectral degeneracy, known as exceptional point (EP), lies at the heart of various intriguing phenomena in optics, acoustics, and other nonconservative systems. Despite extensive studies in the past two decades, the \textit{collective} behaviors (e.g., annihilation, coalescence, braiding, etc.) involving multiple exceptional points or lines and their interplay have been rarely understood. Here we put forward a universal non-Abelian conservation rule governing these collective behaviors in generic multiband non-Hermitian systems and uncover several counterintuitive phenomena. We demonstrate that two EPs with opposite charges (even the pairwise created) do not necessarily annihilate, depending on how they approach each other. Furthermore, we unveil that the conservation rule imposes strict constraints on the permissible exceptional-line configurations. It excludes structures like Hopf link yet permits novel staggered rings composed of noncommutative exceptional lines. These intriguing phenomena are illustrated by concrete models which could be readily implemented in platforms like coupled acoustic cavities, optical waveguides, and ring resonators. Our findings lay the cornerstone for a comprehensive understanding of the exceptional non-Abelian topology and shed light on the versatile manipulations and applications based on exceptional degeneracies in nonconservative systems.

cond-mat.mes-hall↗

arXiv2022

Observation of size-dependent boundary effects in non-Hermitian electric circuits

The non-Hermitian systems with the non-Hermitian skin effect (NHSE) are very sensitive to the imposed boundary conditions and lattice size, which leads to size-dependent non-Hermitian skin effects. Here, we report the experimental observation of NHSE with different boundary conditions and different lattice size in a unidirectional hopping model based on a circuit platform. The circuit admittance spectra and corresponding eigenstates are very sensitive to the presence of the boundary. Meanwhile, our experimental results show how the lattice size and boundary terms together affect the strength of NHSE. Therefore, our electric circuit provides a good platform to observe size-dependent boundary effects in non-Hermitian systems.

quant-ph↗

arXiv2022

Exact solutions of non-Hermitian chains with asymmetric long-range hopping under specific boundary conditions

We study one-dimensional general non-Hermitian models with asymmetric long-range hopping and explore to analytically solve the systems under some specific boundary conditions. Although the introduction of long-range hopping terms prevents us from finding analytical solutions for arbitrary boundary parameters, we identify the existence of exact solutions when the boundary parameters fulfill some constraint relations, which give the specific boundary conditions. Our analytical results show that the wave functions take simple forms and are independent of hopping range, while the eigenvalue spectra display rich model-dependent structures. Particularly, we find the existence of a special point coined as pseudo-periodic boundary condition, for which the eigenvalues are the same as the periodical system when the hopping parameters fulfill certain conditions, whereas eigenstates display non-Hermitian skin effect.

cond-mat.stat-mech↗

arXiv2021

Defective Majorana zero modes in non-Hermitian Kitaev chain

Topological stability is an important property for topological materials. However, the non-Hermitian effects may change this situation. Here, we investigate the robustness of edge states in the non-Hermitian Kitaev chain with imbalanced tunneling term and superconducting pairing term. By defining the similarity of Majorana zero modes (MZMs) and magnetic factor, the coalescing phase diagram of the MZMs and corresponding spin polarization phase diagram are provided. Because of the non-Hermitian coalescence effect and non-Hermitian suppression effect induced by the breakdown of sublattice symmetry and particle-hole symmetry, the system emergence very interesting phenomenons, such as defective MZMs, number-anomalous bulk-boundary correspondence, coalescing of many-body ground states, the magnetic phase crossover without gap closing. Those novel non-Hermitian effects offer fresh insights into MZMs and topological physics.

cond-mat.supr-con↗

arXiv2021

Irrational Non-Abelian Statistics for Non-Hermitian Generalization of Majorana Zero Modes

In condensed matter physics, non-Abelian statistics for Majorana zero modes (or Majorana Fermions) is very important, really exotic, and completely robust. The race for searching Majorana zero modes and verifying the corresponding non-Abelian statistics becomes an important frontier in condensed matter physics. In this letter, we generalize the Majorana zero modes to non-Hermitian (NH) topological systems that show universal but quite different properties from their Hermitian counterparts. Based on the NH Majorana zero modes, the orthogonal and nonlocal Majorana qubits are well defined. In particular, due to the particle-hole-symmetry breaking, NH Majorana zero modes have irrational non-Abelian statistics with continuously tunable braiding Berry phase from pi/8 to 3pi/8. This is quite different from the usual non-Abelian statistics with fixed braiding Berry phase pi/4 and becomes an example of "irrational topological phenomenon". The one-dimensional NH Kitaev model is taken as an example to numerically verify the irrational non-Abelian statistics for two NH Majorana zero modes. The numerical results are exactly consistent with the theoretical prediction. With the help of braiding these two zero modes, the pi/8 gate can be reached and thus universal topological quantum computation becomes possible.

cond-mat.mes-hall↗

arXiv2021

Exact solution of non-Hermitian systems with generalized boundary conditions: size-dependent boundary effect and fragility of skin effect

Systems with non-Hermitian skin effects are very sensitive to the imposed boundary conditions and lattice size, and thus an important question is whether non-Hermitian skin effects can survive when deviating from the open boundary condition. To unveil the origin of boundary sensitivity, we present exact solutions for one-dimensional non-Hermitian models with generalized boundary conditions and study rigorously the interplay effect of lattice size and boundary terms. Besides the open boundary condition, we identify the existence of non-Hermitian skin effect when one of the boundary hopping terms vanishes. Apart from this critical line on the boundary parameter space, we find that the skin effect is fragile under any tiny boundary perturbation in the thermodynamic limit, although it can survive in a finite size system. Moreover, we demonstrate that the non-Hermitian Su-Schreieffer-Heeger model exhibits a new phase diagram in the boundary critical line, which is different from either open or periodical boundary case.

quant-ph↗

arXiv2020

Anomalous Spontaneous Symmetry Breaking in non-Hermitian Systems with Biorthogonal Z2-symmetry

Landau's spontaneous symmetry breaking theory is a fundamental theory that describes the collective behaviors in many-body systems. It was well known that for usual spontaneous symmetry breaking in Hermitian systems, the order-disorder phase transition with gap closing and spontaneous symmetry breaking occur at the same critical point. In this paper, we generalized the Landau's spontaneous symmetry breaking theory to the cases in non-Hermitian (NH) many-body systems with biorthogonal Z2 symmetry and tried to discover certain universal features. We were surprised to find that the effect of the NH terms splits the spontaneous biorthogonal Z2 symmetry breaking from a (biorthogonal) order-disorder phase transition with gap closing. The sudden change of similarity for two degenerate ground states indicates a new type of quantum phase transition without gap closing accompanied by spontaneous biorthogonal Z2 symmetry breaking. We will take the NH transverse Ising model as an example to investigate the anomalous spontaneous symmetry breaking. The numerical results were consistent with the theoretical predictions.

cond-mat.str-el↗

arXiv2020

State-dependent Topological Invariants and Anomalous Bulk-Boundary Correspondence in non-Hermitian Topological Systems

The breakdown of the bulk-boundary correspondence in non-Hermitian (NH) topological systems is an open, controversial issue. In this paper, to resolve this issue, we ask the following question: Can a (global) topological invariant completely describe the topological properties of a NH system as its Hermitian counterpart? Our answer is no. One cannot use a global topological invariant (including non-Bloch topological invariant) to accurately characterize the topological properties of the NH systems. Instead, there exist a new type of topological invariants that are absence in its Hermitian counterpart -- the state dependent topological invariants. With the help of the state-dependent topological invariants, we develop a new topological theory for NH topological system beyond the general knowledge for usual Hermitian systems and obtain an exact formulation of the bulk-boundary correspondence, including state-dependent phase diagram, state-dependent phase transition and anomalous transport properties (spontaneous topological current). Therefore, these results will help people to understand the exotic topological properties of various non-Hermitian systems.

cond-mat.mes-hall↗

arXiv2020

Defective Edge states and Anomalous Bulk-boundary Correspondence for Topological Insulators under Non-Hermitian Similarity Transformation

It was known that for non-Hermitian topological systems due to the non-Hermitian skin effect, the bulk-edge correspondence is broken down. In this paper, by using one-dimensional Su-SchriefferHeeger model and two-dimensional (deformed) Qi-Wu-Zhang model as examples, we focus on a special type of non-Hermitian topological system without non-Hermitian skin effect-topological systems under non-Hermitian similarity transformation. In these non-Hermitian systems, the defective edge states and the breakdown of bulk-edge correspondence are discovered. To characterize the topological properties, we introduce a new type of inversion symmetry-protected topological invariant-total Z2 topological invariant. In topological phases, defective edge states appear. With the help of the effective edge Hamiltonian, we find that the defective edge states are protected by (generalized) chiral symmetry and thus the (singular) defective edge states are unstable against the perturbation breaking the chiral symmetry. In addition, the results are generalized to nonHermitian topological insulators with inversion symmetry in higher dimensions. This work could help people to understand the defective edge states and the breakdown of bulk-edge correspondence for non-Hermitian topological systems.

cond-mat.mes-hall↗

arXiv2020

Effective non-Hermitian physics for degenerate ground states of a nonHermitian Ising model with $\mathcal{RT}$ symmetry

In this paper, based on a one-dimensional non-Hermitian spin model with $\mathcal{RT}$-invariant term, we study the non-Hermitian physics for the two (nearly) degenerate ground states. By using the high-order perturbation method, an effective pseudo-spin model is obtained to describe non-Hermitian physics for the two (nearly) degenerate ground states, which are precisely consistent with the numerical calculations. We found that there may exist effective (anti) $\mathcal{PT}$ symmetry for the effective pseudo-spin model of the two (nearly) degenerate ground states. In particular, there exists spontaneous (anti) $\mathcal{PT}$ -symmetry breaking for the topological degenerate ground states with tunable parameters in external fields. We also found that even a very tiny imaginary external field applied will drive $\mathcal{PT}$ phase transition.

cond-mat.stat-mech↗

arXiv2020

Non-Hermitian Avalanche Effect: Non-Perturbative Effect Induced by Local Non-Hermitian Perturbation on a Z2 Topological Order

In this paper, based on a non-Hermitian toric-code model, we surprisingly find that the degeneracy of ground states can be changed by a local non-Hermitian perturbation (even in thermodynamic limit). We call it non-Hermitian avalanche effect. As the physics consequences of the non-Hermitian avalanche effect, a correspondence between bulk quasi-particles and topologically protected degenerate ground states for Z2 topological order is borken down. In addition, the PT symmetry breaking transition of the topologically degenerate ground states subspace can be observed by fidelity susceptibility.

cond-mat.mes-hall↗

arXiv2019

Non-Hermitian Dynamic Strings and Anomalous Topological Degeneracy on non-Hermitian Toric-code Model with Parity-time Symmetry

In this paper, with the help of Hermitian/non-Hermitian dynamic strings, the theory of non-Hermitian topological order is developed based on a non-Hermitian Wen-plaquette model. The effective models for bosonic topological excitations (e-particle and m-particle) are Hermitian tight-binding lattice model; the effective model for fermionic topological excitation (f-particle) becomes a non-Hermitian tight-binding lattice model. In addition, the effective pseudo-spin model for topologically degenerate ground states is derived by calculating the expectation values of Hermitian/non-Hermitian topological closed dynamic strings. For the topologically degenerate ground states of non-Hermitian Wen-plaquette model on an even-by-odd, odd-by-even and odd-by-odd lattice, anomalous topological degeneracy occurs, i.e., the number of the topologically protected ground states may be reduced from 2 to 1. Now, the effective pseudo-spin model turns into the typical PT-symmetric non-Hermitian Hamiltonian with spontaneous PT-symmetry breaking. At exceptional points, the topologically degenerate ground states merge with each other and the topological degeneracy turns into non-Hermitian degeneracy. In the end, the application of the non-Hermitian Z2 topological order and its possible physics realization are discussed.

cond-mat.mes-hall↗