arXiv subjects

Jinghui Pi

Publications and source records attributed to Jinghui Pi.

9 recordsLinked to original sources

arXiv2025

Scaling behavior of dissipative systems with imaginary gap closing

Point-gap topology, characterized by spectral winding numbers, is crucial to non-Hermitian topological phases and dramatically alters real-time dynamics. In this paper, we study the evolution of quantum particles in dissipative systems with imaginary gap closing, using the saddle-point approximation method. For trivial point-gap systems, imaginary gap-closing points can also be saddle points. This leads to a single power-law decay of the local Green's function, with the asymptotic scaling behavior determined by the order of these saddle points. In contrast, for nontrivial point-gap systems, imaginary gap-closing points do not coincide with saddle points in general. This results in a dynamical behavior characterized by two different scaling laws for distinct time regimes. In the short-time regime, the local Green's function is governed by the dominant saddle points and exhibits an asymptotic exponential decay. In the long-time regime, however, the dynamics is controlled by imaginary gap-closing points, leading to a power-law decay envelope. Our findings advance the understanding of quantum dynamics in dissipative systems and provide predictions testable in future experiments.

quant-ph↗

arXiv2025

General theory for geometry-dependent non-Hermitian bands

In two- and higher-dimensional non-Hermitian lattices, systems can exhibit geometry-dependent bands, where the spectrum and eigenstates under open boundary conditions depend on the bulk geometry even in the thermodynamic limit. Although geometry-dependent bands are widely observed, the underlying mechanism for this phenomenon remains unclear. In this work, we address this problem by establishing a higher-dimensional non-Bloch band theory based on the concept of "strip generalized Brillouin zones" (SGBZs), which describe the asymptotic behavior of non-Hermitian bands when a lattice is extended sequentially along its linearly independent axes. Within this framework, we demonstrate that geometry-dependent bands arise from the incompatibility of SGBZs and, for the first time, derive a general criterion for the geometry dependence of non-Hermitian bands: non-zero area of the complex energy spectrum or the imaginary momentum spectrum. Our work opens an avenue for future studies on the interplay between geometric effects and non-Hermitian physics, such as non-Hermitian band topology.

cond-mat.mes-hall↗

arXiv2025

Geometric origin of self-intersection points in non-Hermitian energy spectra

Unlike Hermitian systems, non-Hermitian energy spectra under periodic boundary conditions can form closed loops in the complex energy plane, a phenomenon known as point gap topology. In this paper, we investigate the self-intersection points of such non-Hermitian energy spectra and reveal their geometric origins. We rigorously demonstrate that these self-intersection points result from the intersection of the auxiliary generalized Brillouin zone and the Brillouin zone in one-band systems, as confirmed by an extended Hatano-Nelson model. This finding is further generalized to multi-band systems, illustrated through a non-Hermitian Su-Schrieffer-Heeger model. Moreover, we address multiple self-intersection points and derive the geometric conditions for general n-fold self-intersection points. Our results enhance the fundamental understanding of generic non-Hermitian quantum systems and provide theoretical support for further experimental investigations of energy self-intersection points.

quant-ph↗

arXiv2024

Investigation of reentrant localization transition in one-dimensional quasi-periodic lattice with long-range hopping

Reentrant localization has recently been observed in systems with quasi-periodic nearest-neighbor hopping, where the interplay between dimerized hopping and staggered disorder is identified as the driving mechanism. However, the robustness of reentrant localization in the presence of long-range hopping remains an open question. In this work, we investigate the phenomenon of reentrant localization in systems incorporating long-range hopping. Our results reveal that long-range hopping induces reentrant localization regardless of whether the disorder is staggered or uniform. We demonstrate that long-range hopping does not inherently disrupt localization; instead, under specific conditions, it facilitates the emergence of reentrant localization. Furthermore, by analyzing critical exponents, we show that the inclusion of long-range hopping modifies the critical behavior, leading to transitions that belong to distinct universality classes.

cond-mat.dis-nn↗

arXiv2024

Topological phases of extended Su-Schrieffer-Heeger-Hubbard model

Despite extensive studies on the one-dimensional Su-Schrieffer-Heeger-Hubbard (SSHH) model, the variant incorporating next-nearest neighbour hopping remains largely unexplored. Here, we investigate the ground-state properties of this extended SSHH model using the constrained-path auxiliary-field quantum Monte Carlo (CP-AFQMC) method. We show that this model exhibits rich topological phases, characterized by robust edge states against interaction. We quantify the properties of these edge states by analyzing spin correlation and second-order R\'enyi entanglement entropy. The system exhibits long-range spin correlation and near-zero R\'enyi entropy at half-filling. Besides, there is a long-range anti-ferromagnetic order at quarter-filling. Interestingly, an external magnetic field disrupts this long-range anti-ferromagnetic order, restoring long-range spin correlation and near-zero R\'enyi entropy. Furthermore, our work provides a paradigm studying topological properties in large interacting systems via the CP-AFQMC algorithm.

cond-mat.str-el↗

arXiv2024

Imaginary-Stark Skin Effect

A unique phenomenon in non-Hermitian systems is the non-Hermitian skin effect (NHSE), namely the boundary localization of continuous-spectrum eigenstates. However, studies on the NHSE in systems without translational invariance are still limited. Here, we unveil a new class of NHSE, dubbed the imaginary-Stark skin effect (ISSE), in a one-dimensional lossy lattice with a spatially increasing loss rate. This ISSE is beyond the framework of non-Bloch band theory and exhibits intriguing properties significantly different from the conventional NHSE. Specifically, the energy spectrum of our model has a T-shaped feature, with approximately half of the eigenstates localized at the left boundary. Furthermore, each skin mode can be expressed as a single stable, exponentially-decaying wave within the bulk region. Such peculiar behaviors are analyzed via the transfer-matrix method, whose eigendecomposition quantifies the formation of the ISSE. Our work provides new insights into the NHSE in systems without translational symmetry and contributes to the understanding of non-Hermitian systems.

quant-ph↗

arXiv2024

Imaginary gap-closed points and dynamics in a class of dissipative systems

We investigate imaginary gap-closed (IGC) points and their associated dynamics in dissipative systems. In a general non-Hermitian model, we derive the equation governing the IGC points of the energy spectrum, establishing that these points are only determined by the Hermitian part of the Hamiltonian. Focusing on a class of one-dimensional dissipative chains, we explore quantum walks across different scenarios and various parameters, showing that IGC points induce a power-law decay scaling in bulk loss probability and trigger a boundary phenomenon referred to as "edge burst". This observation underscores the crucial role of IGC points under periodic boundary conditions (PBCs) in shaping quantum walk dynamics. Finally, we demonstrate that the damping matrices of these dissipative chains under PBCs possess Liouvillian gapless points, implying an algebraic convergence towards the steady state in long-time dynamics.

quant-ph↗

arXiv2024

Extended imaginary gauge transformation in a general nonreciprocal lattice

Imaginary gauge transformation (IGT) provides a clear understanding of the non-Hermitian skin effect by transforming the non-Hermitian Hamiltonians with real spectra into Hermitian ones. In this paper, we extend this approach to the complex spectrum regime in a general nonreciprocal lattice model. We unveil the validity of IGT hinges on a class of pseudo-Hermitian symmetry. The generalized Brillouin zone of Hamiltonians respect such pseudo-Hermiticity is demonstrated to be a circle, which enables easy access to the continuum bands, localization length of skin modes, and relevant topological numbers. Furthermore, we investigate the applicability of IGT and the underlying pseudo-Hermiticity beyond nearest-neighbor hopping, offering a graphical interpretation. Our theoretical framework is applied to establish bulk-boundary correspondence in the nonreciprocal trimer Su-Schrieffer-Heeger model and to analyze the localization behaviors of skin modes in the two-dimensional Hatano-Nelson model.

quant-ph↗

arXiv2023

Investigation of a non-Hermitian edge burst with time-dependent perturbation theory

Edge burst is a phenomenon in non-Hermitian quantum dynamics discovered by a recent numerical study [W.-T. Xue, et al, Phys. Rev. Lett 2, 128.120401(2022)]. It finds that a large proportion of particle loss occurs at the system boundary in a class of non-Hermitian quantum walk. In this paper, we investigate the evolution of real-space wave functions for this lattice system. We find the wave function of the edge site is distinct from the bulk sites. Using time-dependent perturbation theory, we derive the analytical expression of the real-space wave functions and find that the different evolution behaviors between the edge and bulk sites are due to their different nearest-neighbor site configurations. We also find the edge wave function primarily results from the transition of the two nearest-neighbor non-decay sites. Besides, the numerical diagonalization shows the edge wave function is mainly propagated by a group of eigen-modes with a relatively large imaginary part. Our work provides an analytical method for studying non-Hermitian quantum dynamical problems.

quant-ph↗