Large deviations and conditioned monitored quantum systems: a tensor network approach

TL;DR

This paper introduces a tensor network method to analyze large deviations and phase coexistence in monitored quantum many-body systems, revealing first-order dynamical phase transitions and enabling microscopic characterization of phases.

Contribution

It develops a tensor network framework for large deviation analysis in quantum systems, allowing systematic study of dynamical phase coexistence and conditioned states.

Findings

Identified first-order dynamical phase transitions in monitored quantum dynamics.

Provided a method to access large-deviation statistics and conditioned quantum states.

Enabled microscopic characterization of dynamical phases and their coexistence.

Abstract

Coexistence of different dynamical phases is a hallmark of glassy dynamics. This is well-studied in classical systems where the underlying theoretical framework is that of large deviation theory. The presence of a similar phase coexistence has been suggested in monitored quantum many-body systems, but the lack of suitable methods has yet prevented a systematic large deviation analysis. Here we present a tensor network framework that allows the application of large deviation theory to large quantum systems. Building on this, we locate a series of first-order dynamical phase transitions in a monitored discrete-time many-body quantum dynamics, at the level of the trajectory space. Crucially, our approach provides access not only to large-deviation statistics but also to conditioned quantum many-body states, enabling a microscopic characterization of the dynamical phases and their coexistence.