Entanglement view of dynamical quantum phase transitions

TL;DR

This paper classifies dynamical quantum phase transitions (DQPTs) using matrix product states, distinguishing between precession and entanglement types, and explores their properties and implications in quantum many-body dynamics.

Contribution

It introduces a classification scheme for DQPTs based on entanglement properties and provides analytical descriptions in the quantum Ising model.

Findings

Precession DQPTs have a large entanglement gap and are semiclassical.

Entanglement DQPTs occur near avoided crossings in the entanglement spectrum.

The classification extends beyond the Ising model and relates to complex DQPT phenomenology.

Abstract

The analogy between an equilibrium partition function and the return probability in many-body unitary dynamics has led to the concept of dynamical quantum phase transition (DQPT). DQPTs are defined by non-analyticities in the return amplitude and are present in many models. In some cases DQPTs can be related to equilibrium concepts such as order parameters, yet their universal description is an open question. In this work we provide first steps towards a classification of DQPTs by using a matrix product state description of unitary dynamics in the thermodynamic limit. This allows us to distinguish the two limiting cases of precession and entanglement DQPTs, which are illustrated using an analytical description in the quantum Ising model. While precession DQPTs are characterized by a large entanglement gap and are semiclassical in their nature, entanglement DQPTs occur near avoided crossings in the entanglement spectrum and can be distinguished by a complex pattern of non-local correlations. We demonstrate the existence of precession and entanglement DQPTs beyond Ising model, discuss observables that can distinguish them and relate their interplay to complex DQPT phenomenology.