Quantum feedback induced entanglement relaxation and dynamical phase transition in monitored free fermion chains with Wannier-Stark ladder

TL;DR

This paper studies a dynamical phase transition in a monitored free-fermion chain with feedback, revealing a feedback-induced skin effect and unique entanglement dynamics influenced by Wannier-Stark ladder potential.

Contribution

It uncovers the feedback-induced skin effect and characterizes the associated dynamical phase transition in a tilted free-fermion chain with measurement-feedback protocols.

Findings

Identification of a feedback-induced skin effect localized at one boundary.

Observation of a two-stage entanglement evolution: rapid growth then decay.

Critical behavior linked to feedback-driven suppression of quantum fluctuations.

Abstract

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 pseudo edge 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.