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arXiv:2311.16541 · Physical Review Letters

Dynamical Transition Due to Feedback-Induced Skin Effect

Ze-Chuan Liu, Kai Li, Yong Xu

Published Aug 26, 2024• 18 citations
arXivHTMLPDF

Abstract

The traditional dynamical phase transition refers to the appearance of singularities in an observable with respect to a control parameter for a late-time state or singularities in the rate function of the Loschmidt echo with respect to time. Here, we study the many-body dynamics in a continuously monitored free fermion system with conditional feedback under open boundary conditions. We surprisingly find a novel dynamical transition from a logarithmic scaling of the entanglement entropy to an area-law scaling as time evolves. The transition, which is noticeably different from the conventional dynamical phase transition, arises from the competition between the bulk dynamics and boundary skin effects. In addition, we find that while quasidisorder or disorder cannot drive a transition for the steady state, a transition occurs for the maximum entanglement entropy during the time evolution, which agrees well with the entanglement transition for the steady state of the dynamics under periodic boundary conditions.

DOI
10.1103/physrevlett.133.090401

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The traditional dynamical phase transition refers to the appearance of singularities in an observable with respect to a control parameter for a late-time state or singularities in the rate function of the Loschmidt echo with respect to time. Here, we study the many-body dynamics in a continuously monitored free fermion system with conditional feedback under open boundary conditions. We surprisingly find a novel dynamical transition from a logarithmic scaling of the entanglement entropy to an area-law scaling as time evolves. The transition, which is noticeably different from the conventional dynamical phase transition, arises from the competition between the bulk dynamics and boundary skin effects. In addition, we find that while quasidisorder or disorder cannot drive a transition for the steady state, a transition occurs for the maximum entanglement entropy during the time evolution, which agrees well with the entanglement transition for the steady state of the dynamics under periodic boundary conditions.
In recent years, measurement induced entanglement transitions (MIETs) have attracted significant attention. However, the dynamical transition associated with the feedback induced skin effect, which exhibits a wealth of intriguing phenomena, has not been fully understood. In this work, we investigate a dynamical phase transition in a tilted free-fermion chain under measurement-feedback protocols, emphasizing the particle density and entanglement entropy dynamics. We reveal a feedback induced skin effect, enhanced by the Wannier-Stark ladder potential, that creates localization at one boundary and generates an effective pseudoedge under periodic conditions. The observables show a two-stage evolution: a rapid initial logarithmic growth followed by decay into an area-law steady state. Using a rescaling analysis, we pinpoint the critical behavior and offer an intuitive physical picture that links it to the feedback-driven suppression of quantum jump fluctuations. The resulting entanglement dynamics appear to be governed by a system-size-dependent delay, followed by a size-independent relaxation process. This behavior is consistent with the ballistic propagation of free fermions toward a domain-wall-like steady state and does not exhibit any signatures of nontrivial criticality. This work provides an effective supplement to the dynamical transition. It provides valuable references for linking the dynamical understanding of the role feedback plays in MIETs.
Measurement-induced phase transitions in the presence of competition between projective measurement and random unitary evolution have attracted increasing attention due to the rich phenomenology of entanglement structures. However, in open quantum systems with free fermions, a generalized measurement with conditional feedback can induce the skin effect and render the system short-range entangled without any entanglement transition, meaning the system always remains in the ``area law'' entanglement phase. In this work, we demonstrate that power-law long-range hopping does not alter the absence of entanglement transition brought on by the measurement-induced skin effect for systems with open boundary conditions. In addition, for finite-size systems, we discover an algebraic scaling $S(L,L/4)\ensuremath{\sim}{L}^{3/2\ensuremath{-}p}$ when the power-law exponent ppp of long-range hopping is relatively small. For systems with periodic boundary conditions, we find that the measurement-induced skin effect disappears and observe entanglement phase transitions among ``algebraic law,'' ``logarithmic law,'' and ``area law'' phases.
A quantum many-body system subject to unitary evolution and repeated local measurements with an increasing rate undergoes a measurement-induced entanglement transition from extensive (or subextensive) to area law entropy scaling. We find that certain open boundary systems under ``generalized monitoring,'' consisting of ``projective monitoring'' and conditional feedback, display an anomalous late-time particle concentration on the edge, reminiscent of the ``skin effect'' in non-Hermitian systems. Such feedback-induced skin effect will suppress the entanglement generation, rendering the system short-range entangled without measurement-induced entanglement transition. While initially emerged in noninteracting models, such skin effect can also occur in chaotic interacting systems and Floquet quantum circuits subjected to random generalized measurements. Since the dynamics of the skin effect do not require postselection and can be observed at the particle number level, the phenomenon is experimentally relevant and accessible in noisy intermediate-scale quantum platforms, such as trapped ions.
We study the entanglement dynamics of a one-dimensional chain of monitored non-interacting complex fermions with random power-law hopping characterized by a decay exponent ααα. For α≲1α\lesssim 1α≲1, in stark contrast with the case of hopping to nearest neighbors, the scaling of the entanglement entropy (EE) of the steady state with system size LLL is faster than logarithmic for any monitoring or disorder strength and it tends towards a linear (volume-law) scaling for sufficiently small α≲1/2α\lesssim 1/2α≲1/2. For α>3/2α> 3/2α>3/2, the EE is in the area-law phase, namely, no scaling with LLL, for any monitoring strength. For 1<α≲3/21 < α\lesssim 3/21<α≲3/2, we identify an ααα-dependent measurement-induced phase transition (MIPT) at a critical value of the monitoring strength separating the mentioned area-law and sub-volume-law phases. At this critical point, the EE scales logarithmically with system size, and the density-density correlation function, closely related to the EE, exhibits multifractal features. These results highlight the importance of superdiffusive classical hopping in the entanglement dynamic of quantum many-body systems and also help differentiate its role with respect to conventional sources of entanglement such as genuine quantum non-locality.
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.
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.