Dynamical Quantum Phase Transitions in Systems with Continuous Symmetry Breaking

TL;DR

This paper investigates dynamical quantum phase transitions in the three-dimensional O(N) model, revealing that kink singularities in the Loschmidt echo occur at zero-crossings of the order parameter, linked to symmetry-breaking dynamics.

Contribution

It analytically demonstrates the occurrence of dynamical phase transitions with kink singularities in a 3D O(N) model with continuous symmetry breaking, generalizing previous results.

Findings

Kink singularities in the Loschmidt echo occur at zero-crossings of the order parameter.

Dynamical transition separates phases with finite and vanishing order parameter.

Results are applicable to generic systems with continuous symmetry breaking.

Abstract

Interacting many-body systems that are driven far away from equilibrium can exhibit phase transitions between dynamically emerging quantum phases, which manifest as singularities in the Loschmidt echo. Whether and under which conditions such dynamical transitions occur in higher-dimensional systems with spontaneously broken continuous symmetries is largely elusive thus far. Here, we study the dynamics of the Loschmidt echo in the three dimensional O(N) model following a quantum quench from a symmetry breaking initial state. The O(N) model exhibits a dynamical transition in the asymptotic steady state, separating two phases with a finite and vanishing order parameter, that is associated with the broken symmetry. We analytically calculate the rate function of the Loschmidt echo and find that it exhibits periodic kink singularities when this dynamical steady-state transition is crossed. The singularities arise exactly at the zero-crossings of the oscillating order parameter. As a consequence, the appearance of the kink singularities in the transient dynamics is directly linked to a dynamical transition in the order parameter. Furthermore, we argue, that our results for dynamical quantum phase transitions in the O(N) model are general and apply to generic systems with continuous symmetry breaking.