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arXiv:2212.01001 · International Conference on Low Temperature Physics (LT)

Wave-packet and Entanglement Dynamics in a Non-Hermitian Many-body System

Takahiro Orito, Ken‐Ichiro Imura

Published May 22, 2023• 2 citations
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Abstract

The static and dynamical properties of a one-dimensional quantum system described by a non-Hermitian Hamiltonian of the so-called Hatano-Nelson type; a tight-binding model with asymmetric (or non-reciprocal) hopping, are studied.The static properties of the model have been much studied; the complex spectrum, skin effect and its topological interpretation, etc. Effects of disorder and interparticle interaction, especially, when they coexist, may be less understood.Here, we will also focus on its dynamical properties and reveal some unique features in the wave-packet and entanglement (entropy) dynamics.For that some latest (original) results based on improved numerics (with this a system of larger system size L becomes accessible) are shown.

DOI
10.7566/jpscp.38.011187

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The static and dynamical properties of a one-dimensional quantum system described by a non-Hermitian Hamiltonian of the so-called Hatano-Nelson type; a tight-binding model with asymmetric (or non-reciprocal) hopping, are studied.The static properties of the model have been much studied; the complex spectrum, skin effect and its topological interpretation, etc. Effects of disorder and interparticle interaction, especially, when they coexist, may be less understood.Here, we will also focus on its dynamical properties and reveal some unique features in the wave-packet and entanglement (entropy) dynamics.For that some latest (original) results based on improved numerics (with this a system of larger system size L becomes accessible) are shown.
The entanglement dynamics in a non-Hermitian quantum system is studied numerically and analyzed from the viewpoint of quasiparticle picture. As a concrete model, we consider a one-dimensional tight-binding model with asymmetric hopping (Hatano-Nelson model) under onsite disorder and nearest-neighbor interaction. As opposed to an assertion of previous studies, the entanglement dynamics in this non-Hermitian quantum system is very different from the one in its Hermitian counterpart, especially in the delocalized regime with weak disorder; there the entanglement entropy Sent(t){S}_{\mathrm{ent}}(t)Sent​(t) shows a characteristic nonmonotonic time evolution. We have clarified and quantified the nature of this behavior in the quasiparticle picture. In the asymptotic regime of $t\ensuremath{\rightarrow}\ensuremath{\infty}$, the entanglement entropy Sent(t){S}_{\mathrm{ent}}(t)Sent​(t) in this regime saturates to a much suppressed value, which increases only logarithmically with respect to the size of the subsystem.
Non-Hermiticity and dephasing, collaborating in an unusual wave-packet dynamics, realize unconventional entanglement evolution in a disordered, interacting, and asymmetric (nonreciprocal) quantum medium. Taking the Hatano-Nelson model as a concrete example, we first consider how wave packet spreads in a non-Hermitian disordered system for demonstrating that it is very different from the Hermitian case. Interestingly, a cascadelike wave-packet spreading as in the Hermitian case is suppressed in the clean limit and at weak disorder, while it revives in the vicinity of the localization-delocalization transition. Based on this observation, we then analyze how the entanglement entropy of the system evolves in the interacting non-Hermitian model, revealing its nonmonotonic evolution in time. We clarify the different roles of dephasing in the time evolution of entanglement entropy in Hermitian and non-Hermitian systems, and show that the many-body dynamics is governed by a principle different from the Hermitian case. The size dependence of the results suggests with the increase of disorder, an unusual area-volume--area-law crossover of the maximal entanglement entropy. To analyze the effects of disorder on a firm basis, using the Hermitian limit as a benchmark, we employ a quasiperiodic disorder (Aubry-Andr\'e model) in the analyses.
Non-Hermitian dynamics is ubiquitous in various physical systems. While recent study shows that such a dynamics leads to an area-law scaling of the entanglement entropy due to the non-Hermitian skin effects, it remains unclear how disorder changes the behavior of the entanglement entropy in a non-Hermitian system with skin effects. Here we study the dynamics of a many-body state of free fermions in the paradigmatic Hatano-Nelson model with open boundaries, and find that the area-law behavior of the entanglement entropy in the pristine Hatano-Nelson model develops into a logarithmic scaling for small disorder strength. As we further increase the disorder strength, the system reenters an area-law regime through an entanglement phase transition. At the critical point, the entanglement entropy exhibits a universal algebraic scaling. We further demonstrate the absence of a conformal invariance in the log-law regime by examining the subsystem entanglement entropy, the connected correlation function and the mutual information. Finally, we show the existence of disorder induced entanglement phase transitions in the Hatano-Nelson model with periodic boundaries.
Diffusion, dephasing and non-Hermiticity collaborate and realize an unconventional entanglement dynamics in a disordered, interacting and asymmetric (non-reciprocal) quantum media. Taking the Hatano-Nelson model as a concrete example, we first consider how diffusion occurs in a non-Hermitian disordered system for demonstraing that it is very different from the Hermitian case. Interestingly, a cascade like diffusion process as in the Hermitian case is suppressed in the clean limit and at weak disorder, while it revives in the vicinity of the localization-delocalization transition. Based on this observation, we then analyze how the entanglement entropy of the system evolves in the interacting non-Hermitian model, revealing its non-monotonic evolution in time. We clarify the different roles of dephasing in the time evolution of entanglement entropy in Hermitian and non-Hermitian systems, and show that the many-body dynamics is governed by a principle different from the Hermitian case. The size dependence of the results suggests with the increase of disorder, a (reentrant) area-volume-area law crossover of the maximal entanglement entropy. To analyze the effects of disorder on a firm basis, using the Hermitian limit as a benchmark, we employ a quasi-periodic disorder (Aubry-Andr\'{e} model) in the analyses.
This paper investigates wave-packet dynamics in non-Hermitian lattice systems and reveals a surprising phenomenon: The simultaneous propagation of two distinct wavefronts, one traveling at the non-Hermitian velocity and the other at the Hermitian velocity. We show that this dual-front behavior arises naturally in systems governed by a pseudo-Hermitian Hamiltonian. Using the paradigmatic Hatano-Nelson model as our primary example, we demonstrate that this coexistence is essential for understanding a wide array of unconventional dynamical effects, including abrupt ``non-Hermitian reflections'', sudden shifts of Gaussian wave-packets, and disorder-induced emergent packets seeded by the small initial tails. We present analytic predictions that closely match numerical simulations. These results may offer new insight into the topology of non-Hermitian systems and point toward measurable experimental consequences.
The non-Hermitian skin effect, namely, that the eigenvalues and eigenstates of a non-Hermitian tight-binding Hamiltonian have significant differences under open or periodic boundary conditions, is a remarkable phenomenon of non-Hermitian systems. Inspired by the presence of the non-Hermitian skin effect, we study the evolution of wave packets in non-Hermitian systems, which can be determined using the single-particle Green's function. Surprisingly, we find that in the thermodynamic limit, the Green's function does not depend on boundary conditions, despite the presence of skin effect. We provide a general proof for this statement in arbitrary dimension with finite hopping range, with an explicit illustration in the non-Hermitian Su-Schrieffer-Heeger model. We also explore its applications in noninteracting open quantum systems described by the master equation. We demonstrate that the evolution of the density matrix is independent of the boundary condition.