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arXiv:2309.03546 · Physical review. B./Physical review. B

Emergent entanglement phase transitions in non-Hermitian Aubry-André-Harper chains

Shan-Zhong Li, Xue-Jia Yu, Zhi Li

Published Jan 16, 2024• 50 citations
arXivHTMLPDF

Abstract

We investigate the entanglement dynamics of the non-Hermitian Aubry-Andr\'e-Harper chain. The results reveal that by increasing quasiperiodic strength, a phase transition occurs from the area law induced by non-Hermitian skin effect to the area law arising from Anderson localization. For the former, the entanglement entropy follows a nonmonotonic process, i.e., it increases first, then oscillates, and finally converges to a stable value while, for the latter, the entanglement entropy remains low because the wave function is not expandable in Anderson's localization region. The early-stage behavior of entanglement entropy indicates that the two area-law cases are of different phases. Interestingly, the volume-law behavior emerges at the critical point between these two area-law phases. Our study reveals that the area laws induced by the skin effect and the Anderson localization are two different phases, and that a volume law can emerge at the phase transition point. The understanding of the entanglement phase transition induced by disorder and skin effect is thus deepened.

DOI
10.1103/physrevb.109.024306

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We investigate the entanglement dynamics of the non-Hermitian Aubry-Andr'e-Harper chain. The results reveal that by increasing quasiperiodic strength, a phase transition occurs from the area law induced by non-Hermitian skin effect to the area law arising from Anderson localization. For the former, the entanglement entropy follows a nonmonotonic process, i.e., it increases first, then oscillates, and finally converges to a stable value while, for the latter, the entanglement entropy remains low because the wave function is not expandable in Anderson's localization region. The early-stage behavior of entanglement entropy indicates that the two area-law cases are of different phases. Interestingly, the volume-law behavior emerges at the critical point between these two area-law phases. Our study reveals that the area laws induced by the skin effect and the Anderson localization are two different phases, and that a volume law can emerge at the phase transition point. The understanding of the entanglement phase transition induced by disorder and skin effect is thus deepened.
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.
We investigate the interplay between the non-Hermitian skin effect and Aubry-André-Harper (AAH) quasiperiodic disorder in a one-dimensional Su-Schrieffer-Heeger (SSH) chain with nonreciprocal hopping. By exact diagonalization, transfer-matrix analysis, and an analytical similarity-transformation argument, we map the full ( , δδδ) phase diagram, where A is the AAH modulation strength and the nonreciprocity parameter. We identify five distinct regimes: ( ) topological with extended bulk, (II) AAH-localized, (III) skin-localized, (IV) fully localized, and a previously unreported (V) competition regime exhibiting reentrant partial delocalization, in which intermediate quasiperiodic disorder disrupts the directional skin accumulation before ultimately Anderson-localizing all states. Using phase-averaged diagnostics and finite-size scaling, we confirm that the reentrant regime is robust, characterized by a non-monotonic inverse participation ratio that sharpens with increasing system size. We derive an analytical expression for the modified localization boundary λc(δ)=2veffwλ_{c}(δ)=2\sqrt{v_{eff}w}λc​(δ)=2veff​w​ with vvff=v2−δ2v_{vff}=\sqrt{v^{2}-δ^{2}}vvff​=v2−δ2​, which agrees with numerical Lyapunov exponent calculations. We further show that quasiperiodic disorder progressively unwinds the complex spectral loops, destroying the point-gap topology at a critical strength distinct from the band-topological transition ; that the skin effect suppresses entanglement entropy to near-zero values while sufficiently strong AAH disorder partially restores it ; and that the SSH sublattice structure absent in the widely studied non-Hermitian AAH chain is essential for producing the five-phase landscape, as demonstrated by direct comparison with the non-dimerized limit.
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.
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.
Recent years have seen remarkable development in open quantum systems effectively described by non-Hermitian Hamiltonians. A unique feature of non-Hermitian topological systems is the skin effect, anomalous localization of an extensive number of eigenstates driven by nonreciprocal dissipation. Despite its significance for non-Hermitian topological phases, the relevance of the skin effect to quantum entanglement and critical phenomena has remained unclear. Here, we find that the skin effect induces a nonequilibrium quantum phase transition in the entanglement dynamics. We show that the skin effect gives rise to a macroscopic flow of particles and suppresses the entanglement propagation and thermalization, leading to the area law of the entanglement entropy in the nonequilibrium steady state. Moreover, we reveal an entanglement phase transition induced by the competition between the unitary dynamics and the skin effect even without disorder or interactions. This entanglement phase transition accompanies nonequilibrium quantum criticality characterized by a nonunitary conformal field theory whose effective central charge is extremely sensitive to the boundary conditions. We also demonstrate that it originates from an exceptional point of the non-Hermitian Hamiltonian and the concomitant scale invariance of the skin modes localized according to the power law. Furthermore, we show that the skin effect leads to the purification and the reduction of von Neumann entropy even in Markovian open quantum systems described by the Lindblad master equation. Our work opens a way to control the entanglement growth and establishes a fundamental understanding of phase transitions and critical phenomena in open quantum systems far from thermal equilibrium.
The Wannier-Stark localization dynamically alters the entanglement behavior of non-Hermitian free fermions. Utilizing the single-particle correlation matrix technique, we analyze the effective Hamiltonian of these fermions with a Wannier-Stark ladder. Under open boundary conditions, we observe steady-state half-chain entanglement entropy (EE) and identify two distinct area-law regions and an algebraic scaling region. Finite-sized scaling analysis reveals critical scaling behavior of the half-chain EE. Notably, the system demonstrates unique entanglement characteristics under periodic boundary conditions, which diverge from the (1+1)d(1+1)d(1+1)d conformal field theory predictions for Anderson localization. Our findings highlight entanglement phases emerging from the interplay between the non-Hermitian skin effect and disorder-free localization.