arXiv subjects

Wen-Tan Xue

Publications and source records attributed to Wen-Tan Xue.

12 recordsLinked to original sources

arXiv2026

Hilbert space connectivity in non-Hermitian many-body systems: emergent scale-dependent amplification and constraint-induced skin localization

Various exotic many-body phenomena such as quantum scars and fractons have been linked to Hilbert space fragmentation. In this work, we find that in non-Hermitian settings, Hilbert space connectivity has an even more universal and fundamental influence, tightly controlling the nature of spectral amplification and state localization. Far more complicated than real-space lattices, non-Hermitian many-body Hilbert space graphs not only possess intricate competing amplification channels, but also global feedback loops connecting remote Fock states related by particle symmetry. These features lead to amplification behavior with unconventional scaling and localization properties. Particle occupation constraints can furthermore remove selected Hilbert space pathways, leading to robust unipolar and asymmetric bipolar skin localization in otherwise reciprocal processes. These results extend beyond simple interacting bosonic models and establish Hilbert space connectivity as a versatile control knob for many-body non-Hermitian critical transitions.

cond-mat.mes-hall↗

arXiv2026

Non-Hermitian Edge State Endocytosis

An isolated edge state observed in a finite open chain is usually expected to survive the thermodynamic limit (TDL), with a localization mechanism distinct from non-Hermitian skin accumulation, which localizes the \emph{entire} bulk continuum. We show that scale-sensitive non-Hermitian systems can generically admit a different fate: as we scale up the system size, a detached edge-localized eigenstate can remain sharply visible over a broad window until a critical scale is reached, where it forms an ephemeral bound state in the continuum (BIC) of the open-boundary bulk before being absorbed (entocytosed) at even larger system sizes. We call this phenomenon edge state endocytosis. Its mechanism is fundamentally traced to the Widom expansion of the open-chain characteristic determinant (energy dispersion equation) into contributions corresponding to admissible non-Bloch mode subsets. Each subset contribution factorizes into a boundary-projected Green's function (proj-GF) determinant, which encodes lattice truncation, and a subset-resolved bulk propagation factor, which encodes the system size dependence. We uncover the fundamental distinction: TDL edge states are zeros of the leading-subset proj-GF determinant, whereas endocytosed states are a hitherto-ignored class of hidden proj-GF zeros from subleading subsets that control the spectrum at finite sizes. Due to its fundamental mathematical origin, the endocytosis mechanism is completely platform-independent, occurring generically without fine-tuning when isolated edge states, topological or otherwise, are subject to non-Hermitian couplings that generate the requisite non-locality. Our new framework quantitatively predicts the endocytosis scale and sheds light on how its intricate competitive mechanism can be revealed through experimentally relevant Green's functions.

cond-mat.mes-hall↗

arXiv2025

Topologically protected negative entanglement

The entanglement entropy encodes fundamental characteristics of quantum many-body systems, and is particularly subtle in non-Hermitian settings where eigenstates generically become non-orthogonal. In this work, we find that negative biorthogonal entanglement generically arises from topologically protected non-orthogonal edge states in free fermion systems, especially for flat-band edge states. Departing from previous literature which associated negative entanglement with exceptional gapless points, we show that robustly negative entanglement can still occur in gapped systems. Gapless 2D flat-band edge states, however, exhibit novel $S_A\sim -\frac{1}{2}L_y^2\log L$ entanglement behavior which scales quadratically with the transverse dimension $L_y$, independent of system parameters. This dramatically negative scaling can be traced to a new mechanism known as non-Hermitian critical skin compression (nHCSC), where topological and skin localization in one direction produces a hierarchy of extensively many probability non-conserving entanglement eigenstates across a cut in another direction. Our discovery sheds light on new avenues where topology interplays with criticality and non-Hermitian localization, unrelated to traditional notions of topological entanglement entropy. This topologically protected negative entanglement also manifests in the second Rényi entropy, which can be measured through SWAP operator expectation values.

quant-ph↗

arXiv2025

Non-Hermitian entanglement dip from scaling-induced exceptional criticality

It is well established that the entanglement entropy of a critical system generally scales logarithmically with system size. Yet, in this work, we report a new class of non-Hermitian critical transitions that exhibit dramatic divergent dips in their entanglement entropy scaling, strongly violating conventional logarithmic behavior. Dubbed scaling-induced exceptional criticality (SIEC), it transcends existing non-Hermitian mechanisms such as exceptional bound states and non-Hermitian skin effect (NHSE)-induced gap closures, which are nevertheless still governed by logarithmic entanglement scaling. Key to SIEC is its strongly scale-dependent spectrum, where eigenbands exhibit an exceptional crossing only at a particular system size. As such, the critical behavior is dominated by how the generalized Brillouin zone (GBZ) sweeps through the exceptional crossing with increasing system size, and not just by the gap closure per se. We provide a general approach for constructing SIEC systems based on the non-local competition between heterogeneous NHSE pumping directions, and show how a scale-dependent GBZ can be analytically derived to excellent accuracy. Beyond 1D free fermions, SIEC is expected to occur more prevalently in higher-dimensional or even interacting systems, where antagonistic NHSE channels generically proliferate. SIEC-induced entanglement dips generalize straightforwardly to kinks in other entanglement measures such as Renyi entropy, and serve as spectacular demonstrations of how algebraic and geometric singularities in complex band structures manifest in quantum information.

quant-ph↗

arXiv2025

Interacting non-Hermitian edge and cluster bursts on a digital quantum processor

A lossy quantum system harboring the non-Hermitian skin effect can in certain conditions exhibit anomalously high loss at the boundaries of the system compared to the bulk, a phenomenon termed the non-Hermitian edge burst. We uncover interacting many-body extensions of the edge burst that are spatially extended and patterned, as well as cluster bursts that occur away from boundaries. Owing to the methodological difficulty and overhead of accurately realizing non-Hermitian dynamical evolution, much less tunable interactions, few experimental avenues in studying the single-particle edge burst have been reported to date and none for many-body variants. We overcome these roadblocks in this study, and present a realization of edge and cluster bursts in an interacting quantum ladder model on a superconducting quantum processor. We utilize a time-stepping algorithm, which implements time-evolution by non-Hermitian Hamiltonians by composing a linear combination of unitaries scheme and product formulae, to assess long-time behavior of the system. We observe signatures of the non-Hermitian edge burst on up to 64 unit cells, and detect the closing of the dissipative gap, a necessary condition for the edge burst, by probing the imaginary spectrum of the system. In suitable interacting regimes, we identify the emergence of spatial patterning and cluster bursts. Beyond establishing these generalized forms of edge burst phenomena, our study paves the way for digital quantum processors to be harnessed as a versatile platform for non-Hermitian condensed-matter physics.

quant-ph↗

arXiv2025

Non-Bloch edge dynamics of non-Hermitian lattices

The non-Hermitian skin effect, i.e., the localization of nominally bulk modes, not only drastically reshapes the spectral properties of non-Hermitian systems, but also dramatically modifies the real-time dynamics therein. Here we investigate the time evolution of waves (or quantum-mechanical particles) initialized around the edge of non-Hermitian lattices. The non-Hermitian skin effect tends to localize the wave to the edge, meaning that the real-time dynamics differs from the Bloch-theory picture. We focus on the long-time decay or growth rate of wave function, which is quantified by the Lyapunov exponents. These exponents can be obtained from the saddle points in the complex momentum space. We propose an efficient yet unambiguous criterion for identifying the dominant saddle point that determines the Lyapunov exponents. Our criterion can be precisely formulated in terms of a mathematical concept known as the Lefschetz thimble. Counterintuitively, the seemingly natural criterion based on the imaginary part of the energy fails. Our work provides a coherent theory for characterizing the real-time edge dynamics of non-Hermitian lattices. Our predictions are testable in various non-Hermitian physical platforms.

quant-ph↗

arXiv2025

Universal scaling of Green's functions in disordered non-Hermitian systems

The competition between non-Hermitian skin effect and Anderson localization leads to various intriguing phenomena concerning spectrums and wavefunctions. Here, we study the linear response of disordered non-Hermitian systems, which is precisely described by the Green's function. We show that the average maximum value of matrix elements of Green's functions, which quantifies the maximal response against an external perturbation, exhibits different phases characterized by different scaling behaviors with respect to the system size. Whereas the exponential-growth phase is also seen in the translation-invariant systems, the algebraic-growth phase is unique to disordered non-Hermitian systems. We explain the numerical findings using the large deviation theory, which provides analytical insights into the algebraic scaling factors of non-Hermitian disordered Green's functions. Furthermore, we show that these scaling behaviors can be observed in the steady states of disordered open quantum systems, offering a quantum-mechanical avenue for their experimental detection. Our work highlights an unexpected interplay between non-Hermitian skin effect and Anderson localization.

cond-mat.mes-hall↗

arXiv2024

Non-Bloch band theory for non-Hermitian continuum systems

One of the most pronounced non-Hermitian phenomena is the non-Hermitian skin effect, which refers to the exponential localization of bulk eigenstates near the boundaries of non-Hermitian systems. Whereas non-Bloch band theory has been developed to describe the non-Hermitian skin effect in lattice systems, its counterpart in continuum systems still lacks a quantitative characterization. Here, we generalize the non-Bloch band theory to non-Hermitian continuum systems. In contrast to lattice systems for which the bulk Hamiltonian alone determines the non-Hermitian skin effect and energy spectrum, we find for continuum systems that the number of boundary conditions, i.e., the number of independent differential equations satisfied by wavefunctions at two boundaries, must also be included as essential information. We show that the appropriate discretization of continuum systems into lattice models requires matching the hopping range of the latter with the number of boundary conditions in the former. Furthermore, in periodic non-Hermitian continuum systems, we highlight the application of the transfer matrix in determining the generalized Brillouin zone. Our theory serves as a useful toolbox for investigating the rich non-Bloch physics in non-Hermitian continuum systems, such as photonic crystals, elastic media, and certain cold-atom systems.

cond-mat.mes-hall↗

arXiv2023

Steady-state edge burst: From free-particle systems to interaction-induced phenomena

The interplay between the non-Hermitian skin effect and the imaginary gap of lossy lattices results in the edge burst, a boundary-induced dynamical phenomenon in which an exceptionally large portion of particle loss occurs at the edge. Here, we find that this intriguing non-Hermitian dynamical phenomenon can be exactly mapped into the steady-state density distribution of a corresponding open quantum system. Consequently, the bulk-edge scaling relation of loss probability in the edge burst maps to that of steady-state density. Furthermore, we introduce a many-body open-system model in which the two-body loss generates an interaction-induced non-Hermitian skin effect. Using the positive-$P$ method, we demonstrate the validity of the scaling relation for steady-state correlators. These results provide a unique perspective on the interaction-induced many-body non-Hermitian skin effect. Our predictions are testable in state-of-the-art experimental platforms.

quant-ph↗

arXiv2023

Observation of non-Hermitian edge burst in quantum dynamics

The non-Hermitian skin effect, by which the eigenstates of Hamiltonian are predominantly localized at the boundary, has revealed a strong sensitivity of non-Hermitian systems to the boundary condition. Here we experimentally observe a striking boundary-induced dynamical phenomenon known as the non-Hermitian edge burst, which is characterized by a sharp boundary accumulation of loss in non-Hermitian time evolutions. In contrast to the eigenstate localization, the edge burst represents a generic non-Hermitian dynamical phenomenon that occurs in real time. Our experiment, based on photonic quantum walks, not only confirms the prediction of the phenomenon, but also unveils its complete space-time dynamics. Our observation of edge burst paves the way for studying the rich real-time dynamics in non-Hermitian topological systems.

cond-mat.mes-hall↗

arXiv2022

Non-Hermitian Edge Burst

We unveil an unexpected non-Hermitian phenomenon, dubbed edge burst, in non-Hermitian quantum dynamics. Specifically, in a class of non-Hermitian quantum walk in periodic lattices with open boundary condition, an exceptionally large portion of loss occurs at the system boundary. The physical origin of this edge burst is found to be an interplay between two unique non-Hermitian phenomena: non-Hermitian skin effect and imaginary gap closing. Furthermore, we establish a universal bulk-edge scaling relation underlying the non-Hermitian edge burst. Our predictions are experimentally accessible in various non-Hermitian systems including quantum-optical and cold-atom platforms.

quant-ph↗

arXiv2021

Simple formulas of directional amplification from non-Bloch band theory

Green's functions are fundamental quantities that determine the linear responses of physical systems. The recent developments of non-Hermitian systems, therefore, call for Green's function formulas of non-Hermitian bands. This task is complicated by the high sensitivity of energy spectrums to boundary conditions, which invalidates the straightforward generalization of Hermitian formulas. Here, based on the non-Bloch band theory, we obtain simple Green's function formulas of general one-dimensional non-Hermitian bands. Furthermore, in the large-size limit, these formulas dramatically reduce to finding the roots of a simple algebraic equation. As an application, our formulation provides the desirable formulas for the defining quantities, the gain and directionality, of directional amplification. Thus, our formulas provide an efficient guide for designing directional amplifiers.

cond-mat.mes-hall↗