Symmetry Breaking Dynamics in Quantum Many-Body Systems

TL;DR

This paper investigates how symmetry breaking and restoration occur dynamically in quantum many-body systems using entanglement asymmetry, revealing unexpected behaviors and quantum Mpemba effects in different scenarios.

Contribution

It introduces the use of entanglement asymmetry to analyze symmetry dynamics in quantum systems, highlighting novel overshooting behavior and the interplay of initial states and Hamiltonians.

Findings

Entanglement asymmetry shows overshooting at early times.

Symmetry can be restored or remain broken depending on the scenario.

Quantum Mpemba effects are observed despite weak symmetry-breaking.

Abstract

Entanglement asymmetry has emerged as a powerful tool for characterizing symmetry breaking in quantum many-body systems. In this Letter, we explore how symmetry is dynamically broken through the lens of entanglement asymmetry in two distinct scenarios: a non-symmetric random quantum circuit and a non-symmetric Hamiltonian quench, with a particular focus on U(1) symmetry. In the former case, the symmetry is initially broken and subsequently restored, whereas in the latter case, symmetry remains broken in the subsystem at late times, consistent with the principles of quantum thermalization. Notably, the growth of entanglement asymmetry exhibits unexpected overshooting behavior at early times in both contexts, contrasting with the behavior of charge variance. We also consider dynamics of non-symmetric initial states under the symmetry-breaking evolution. Due to the competition of symmetry-breaking in both the initial state and Hamiltonian, the early-time entanglement asymmetry can increase and decrease, while quantum Mpemba effects remain evident despite the weak symmetry-breaking in both settings.