Random Quantum Circuits with Time-Reversal Symmetry

TL;DR

This paper introduces a model of random quantum circuits with time-reversal symmetry, analyzing entanglement, chaos, and phase transitions, revealing new universality classes and critical exponents in TR-invariant systems.

Contribution

It develops a statistical mechanics framework for TR-invariant quantum circuits and explores their measurement-induced phase transitions, highlighting the impact of TR-symmetry on universality classes.

Findings

TR-invariance does not affect universality class unless post-selected.

Numerical confirmation of novel critical exponents in TR-invariant systems.

Identification of new universality classes in measurement-induced phase transitions.

Abstract

Time-reversal (TR) symmetry is crucial for understanding a wide range of physical phenomena, and plays a key role in constraining fundamental particle interactions and in classifying phases of quantum matter. In this work, we introduce an ensemble of random quantum circuits that are representative of the dynamics of generic TR-invariant many-body quantum systems. We derive a general statistical mechanics model describing entanglement, many-body quantum chaos and quantum information dynamics in such TR-invariant circuits. As an example of application of our formalism, we study the universal properties of measurement-induced phase transitions (MIPT) in monitored TR-invariant systems, with measurements performed in a TR-invariant basis. We find that TR-invariance of the unitary part of the dynamics does not affect the universality class, unless measurement outcomes are post-selected to satisfy the global TR-invariance of each quantum trajectory. We confirm these predictions numerically, and find, for both generic and Clifford-based evolutions, novel critical exponents in the case of ``strong'', i.e. global TR-invariance where each quantum trajectory is TR-invariant.