System-environment entanglement phase transitions

TL;DR

This paper investigates universal properties and phase transitions of system-environment entanglement in open quantum many-body systems, revealing how measurement influences entanglement and uncovering unconventional behaviors linked to boundary conformal field theory.

Contribution

It introduces a field-theoretical framework connecting entanglement phase transitions to boundary CFT and demonstrates measurement-induced effects on universal entanglement properties.

Findings

Universal entanglement contributions depend on the TLL parameter K.

Measurement strength can cause singularities indicating entanglement phase transitions.

Unconventional increase in entanglement contribution with measurement strength observed.

Abstract

Entanglement in quantum many-body systems can exhibit universal phenomena governed by long-distance properties. We study universality and phase transitions of the entanglement inherent to open many-body systems, namely, the entanglement between a system of interest and its environment. Specifically, we consider the Tomonaga-Luttinger liquid (TLL) under a local measurement and analyze its unconditioned nonunitary evolution, where the measurement outcomes are averaged over. We quantify the system-environment entanglement by the R\'enyi entropy of the post-measurement density matrix, whose size-independent term encodes the universal low-energy physics. We develop a field-theoretical description to relate the universal term to the effective ground-state degeneracy known as the $g$ function in a boundary conformal field theory, and use the renormalization group method to determine its value. We show that the universal contribution is determined by the TLL parameter $K$ and can exhibit singularity signifying an entanglement phase transition. Surprisingly, in certain cases the size-independent contribution can increase as a function of the measurement strength in contrast to what is na\"ively expected from the $g$-theorem. We argue that this unconventional behavior could be attributed to the dangerously irrelevant term which has been found in studies of the resistively shunted Josephson junction. We also check these results by numerical calculations in the spin-$\frac{1}{2}$ XXZ chain subject to a site-resolved measurement. Possible experimental realization in ultracold gases, which requires no postselections, is discussed.