Absence of logarithmic and algebraic scaling entanglement phases due to skin effect

TL;DR

This paper investigates how the measurement-induced skin effect in open quantum systems prevents entanglement phase transitions, and how long-range hopping influences entanglement scaling and phase behavior under different boundary conditions.

Contribution

It demonstrates that long-range hopping does not induce entanglement transitions in systems with skin effect and reveals boundary-condition-dependent entanglement phases.

Findings

Skin effect prevents entanglement transition in open systems.

Long-range hopping does not alter the absence of entanglement transition.

Periodic boundary conditions show multiple entanglement phases.

Abstract

Measurement-induced phase transition in the presence of competition between projective measurement and random unitary evolution has 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 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 the 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 the finite-size systems, we discover an algebraic scaling $S(L, L/4)\sim L^{3/2-p}$ when the power-law exponent $p$ 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.