arXiv subjects

Xiao-Ran Wang

Publications and source records attributed to Xiao-Ran Wang.

7 recordsLinked to original sources

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↗

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

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

Defective Edge States and Anomalous Bulk-Boundary Correspondence in non-Hermitian Topological Systems

Non-Hermitian topological systems show quite different properties as their Hermitian counterparts. An important, puzzled issue on non-Hermitian topological systems is the existence of defective edge states beyond usual bulk-boundary correspondence (BBC) that localize either on the left edge or the right edge of the one-dimensional system. In this paper, to understand the existence of the defective edge states, the theory of anomalous bulk-boundary correspondence (A-BBC) is developed that distinguishes the non-Bloch bulk-boundary correspondence (NB-BBC) from non-Hermitian skin effect. By using the one-dimensional non-Hermitian Su-Schrieffer-Heeger model as an example, the underlying physics of defective edge states is explored. The defective edge states are physics consequence of boundary exceptional points of anomalous edge Hamiltonian. In addition, with the help of a theorem, the number anomaly of the edge states in non-Hermitian topological systems become a mathematic problem under quantitative calculations by identifying the Abelian/non-Abelian non-Hermitian condition for edge Hamiltonian and verifying the deviation of the BBC ratio from 1. In the future, the theory for A-BBC can be generalized to higher dimensional non-Hermitian topological systems (for example, 2D Chern insulator).

cond-mat.str-el↗

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↗