Dynamics of entanglement entropy for a locally monitored lattice gauge theory

TL;DR

This study investigates how continuous local measurements affect entanglement entropy in a 1+1D Z2 lattice gauge theory, revealing no measurement-induced phase transition and providing insights into non-Hermitian quantum dynamics.

Contribution

It models the effects of quantum measurements on a gauge theory using tensor networks, highlighting the absence of measurement-induced phase transitions in entanglement dynamics.

Findings

Entanglement entropy saturates independently of system size at late times.

Continuous monitoring of local observables shows no measurement-induced phase transition.

Tensor network calculations enable probing larger lattice sizes effectively.

Abstract

The $1+1$ dimensional $Z_2$ gauge theory is the simplest model that allows for quantum computation or quantum simulation to probe the fundamental aspects of a gauge theory coupled with dynamical fermions. To reliably benchmark such a system, it is crucial to understand the non-unitary quantum dynamics arising from the underlying non-Hermitian evolution and to model the effects of quantum measurements. This work focuses on monitoring ultra-local physical observables for a $\mathbb Z_2$ gauge theory. Tensor network calculations are performed to dynamically probe entanglement entropy at larger lattice sizes. In this work, we report that continuously monitoring local and diagonal observables (electric and mass energy densities) in the computational basis demonstrates the absence of any measurement-induced phase transition, as indicated by the system-size independence of the late-time saturation value of the bipartite entanglement entropy.