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Unusual diffusion and entanglement dynamics in non-Hermitian disordered many-body systems.

Takahiro Orito, Ken‐Ichiro Imura

Published Sep 28, 2021• 0 citations
OpenAlex

Abstract

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.

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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.
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.
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-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.
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.
Abstract Many-body localized phases retain memory of their initial conditions in disordered interacting systems with unitary dynamics. The stability of the localized phase due to the breakdown of unitarity is of relevance to experiment in the presence of dissipation. Here we investigate the impact of non-Hermitian perturbations on many-body localization. We focus on the interacting Hatano-Nelson model which breaks unitarity via asymmetric hopping. We explore the phase diagram for the mid-spectrum eigenstates as a function of the interaction strength and the non-Hermiticity. In contrast to the non-interacting case, our findings are consistent with a two-step approach to the localized regime. We also study the dynamics of the particle imbalance. We show that the distribution of relaxation time scales differs qualitatively between the localized and ergodic phases. Our findings suggest the possibility of an intermediate dynamical regime in disordered open systems.
The scaling law of entanglement entropy could undergo qualitative changes during the nonunitary evolution of a quantum many-body system. In this work, we uncover such entanglement phase transitions for free fermions in one-dimensional non-Hermitian quasicrystals (NHQCs). We identify two types of entanglement transitions with different scaling laws and critical behaviors due to the interplay between non-Hermitian effects and quasiperiodic potentials. The first type represents a typical volume-law to area-law transition, which happens together with a PT-symmetry breaking and a localization transition. The second type features an abnormal log-law to area-law transition, which is mediated by a critical phase with a volume-law scaling in the steady-state entanglement entropy. These entangling phases and transitions are demonstrated in two representative models of noninteracting NHQCs. Our results thus advance the study of entanglement transitions in non-Hermitian disordered systems and further disclose the rich entanglement patterns in NHQCs.