arXiv subjects

Shu-Xuan Wang

Publications and source records attributed to Shu-Xuan Wang.

8 recordsLinked to original sources

arXiv2026

Mechanism for scale-free skin effect in one-dimensional systems

Non-Hermitian skin effect is one of the most captivating phenomena in non-Hermitian systems, characterized by the extensive localization of eigenstates near open boundaries. In its conventional form, the localization length of a skin mode is independent of the system size. Remarkably, however, when the open boundaries are coupled to realize a generalized boundary condition, the localization length can undergo a drastic transformation, becoming proportional to the system length. This intriguing regime is known as the scale-free skin effect (SFSE). Although SFSE has been observed in numerous one-dimensional non-Hermitian models through case-by-case studies, a unified theoret ical framework capable of predicting its emergence and characteristic properties remains absent. In this work, we take a firm step forward by establishing a model-independent framework for the ana lytic determination of scale-free localization lengths in certain regimes. Our key insight is to treat generalized boundary conditions as a perturbation of the periodic boundary conditions, thereby circumventing the singular response-to-perturbation that would otherwise arise if they were pertur batively treated relative to open boundary conditions. Our work sheds new light on understanding SFSE in non-Hermitian systems.

quant-ph↗

arXiv2025

Theory for the spectral splitting exponent of exceptional points

Exceptional points (EPs), singularities in non-Hermitian systems where eigenvalues and eigenstates coalesce, exhibit a dramatically enhanced response to perturbations compared to Hermitian degeneracies. This makes them exceptional candidates for sensing applications. The spectral splitting of an $N$th-order EP scales with perturbation strength $ε$ over a wide range, from $ε$ to $ε^{1/N}$. Although the exact scaling exponent can be determined in principle by solving the characteristic equation, this approach becomes analytically intractable for large $N$ and often fails to yield useful physical insight. In this work, we develop a theory to directly predict the scaling exponent from the matrix positions of the perturbation. By using the Jordan block structure of the unperturbed Hamiltonian, we show that the splitting exponent can be analytically determined when the matrix positions of the perturbation satisfy some specific conditions. Our analytical framework provides a useful design principle for engineering perturbations to achieve a desired spectral response, facilitating the development of EP-based sensors.

quant-ph↗

arXiv2025

Super-enhanced Sensitivity in Non-Hermitian Systems at Infernal Points

The emergence of exceptional points in non-Hermitian systems represents an intriguing phenomenon characterized by the coalescence of eigenenergies and eigenstates. When a system approaches an exceptional point, it exhibits a heightened sensitivity to perturbations compared to the conventional band degeneracy observed in Hermitian systems. This sensitivity, manifested in the splitting of the eigenenergies, is amplified as the order of the exceptional point increases. Infernal points constitute a unique subclass of exceptional points, distinguished by their order escalating with the expansion of the system's size. In this paper, we show that, when a non-Hermitian system is at an infernal point, a perturbation of strength $ε$, which couples the two opposing boundaries of the system, causes the eigenenergies to split according to the law $\sqrt[k]ε$, where $k$ is an integer proportional to the system's size. Utilizing the perturbation theory of Jordan matrices, we demonstrate that the exceptional sensitivity of the eigenenergies at infernal points to boundary-coupling perturbations is a ubiquitous phenomenon, irrespective of the specific form of the non-Hermitian Hamiltonians. Notably, we find that this phenomenon remains robust even when the system deviates substantially from the infernal point. The universal nature and robustness of this phenomenon suggest potential applications in enhancing sensor sensitivity.

cond-mat.mes-hall↗

arXiv2024

General theory for infernal points in non-Hermitian systems

The coalescence of eigenstates is a unique phenomena in non-Hermitian systems. Remarkably, it has been noticed in some non-Hermitian systems under open boundary conditions that the whole set of eigenstates can coalesce to only a few eigenstates. In the parameter space, the point at which such a coalescence of macroscopic eigenstates occurs is dubbed as an infernal point. In this paper, based on the non-Bloch band theory and amoeba formulation, we establish the criteria for the presence of infernal points in one-dimensional and higher dimensional open-boundary non-Hermitian systems. In addition, we find an explanation of the extreme localization of the wave functions and unveil the mechanism for the coalescence of enormous eigenstates at the infernal points. Our work provides a general theory for infernal points in open-boundary non-Hermitian systems in arbitrary dimensions, and hence paves the way to study the intriguing infernal points systematically.

cond-mat.mes-hall↗

arXiv2024

Constraints of internal symmetry on the non-Hermitian skin effect and bidirectional skin effect under the action of the Hermitian conjugate of time-reversal symmetry

Non-Hermitian skin effect is a basic phenomenon in non-Hermitian system, which means that an extensive number of eigenstates can be localized at the boundary. In this Letter, we systematically investigate the constraints from all internal symmetries on the non-Hermitian skin effect in arbitrary dimensions. By adopting the powerful Amoeba formulation, we build a generic correspondence between the various internal symmetries and the behavior of the non-Hermitian skin effect. Notably, we find that, for non-Hermitian systems with the time-reversal$^\dagger$ symmetry, the eigenstates can simultaneously localize at opposite boundaries, which is beyond the Amoeba formulation, and we dub the phenomenon bidirectional skin effect. Our work provides an overall perspective from the internal symmetry to the non-Hermitian skin effect.

quant-ph↗

arXiv2022

Topological Classification of Gapped/Gap-preserving Rational Space-Time Crystal Systems

The traditional systems researched in condensed matter physics always have spatial translation symmetry. However for space-time crystal systems, the spatial translation symmetry is no longer preserved and the lattice potential have space-time translation symmetry instead. We show that a rational space-time crystal system is equal to a traditional floquet system. Then, we find a way to solve the floquet equation analytically and construct an effective Hamiltonian of the rational space-time crystal system. By this effective Hamiltonian, we obtain the topological classification of gapped and gap-preserving rational space-time crystal systems. Our works reveal the correlation between space-time crystal systems and floquet systems and give a systematic method to explore the properties of rational space-time crystal systems.

cond-mat.mes-hall↗

arXiv2022

Duality between Generalized Non-Hermitian HN Model in Flat Space and Hermitian System in Curved space

Non-Hermitian systems in condensed matter Physics are well studied in recent years. In conventional viewpoint, the non-Hermiticity of a Hamiltonian is obtained by dissipative or gain and loss. Recently, some people investigate the non-Hermiticity from other perspective, which point out that non-Hermiticity may come from the curved space. In this letter, we derive a duality between a generalized non-Hermitian HN model in $d$-dimensional flat space and a Hermitian system in $3d$-dimensional curved space, and give the metric of the curved space analytically. From this duality, we establish a correspondence between Hermitian and non-Hermitian systems, which gives a new perspective to explore non-Hermitian systems.

cond-mat.mes-hall↗

arXiv2020

Network reconstruction from asynchronously updated evolutionary game

The interactions between players of prisoner's dilemma (PD) game are reconstructed with evolutionary game data. All participants play the game with their counterparts and gain corresponding rewards during each round of the game. However, their strategies are updated asynchronously during the evolutionary PD game. Two inference methods of the interactions between players are derived with naive mean-field (nMF) approximation and maximum log-likelihood estimation (MLE) respectively. The two methods are tested numerically also for fully connected asymmetric Sherrington-Kirkpatrick (SK) models, varying the data length, asymmetric degree, payoff and system noise (coupling strength). We find that the reconstruction mean square error (MSE) of MLE method is proportional to the inverse of data length and typically half (benefit from the extra information of update times) of that by nMF. Both methods are robust to the asymmetric degree but works better for large payoff. Compared with MLE, nMF is more sensitive to the couplings strength which prefers weak couplings.

physics.soc-ph↗