Relation between equilibrium quantum phase transitions and dynamical quantum phase transitions in two-band systems

TL;DR

This paper establishes a precise condition linking equilibrium and dynamical quantum phase transitions in two-band systems, using quench fidelity to analyze their relationship with a focus on the 1D anisotropic XY model.

Contribution

It introduces the concept of quench fidelity as a necessary and sufficient condition for DQPTs, clarifying their connection to EQPTs in two-band systems.

Findings

Quench fidelity determines the occurrence of DQPTs.

Delineates the relation between EQPTs and DQPTs.

Analyzes the XY model as an example.

Abstract

The dynamical quantum phase transition (DQPT) is an important concept in nonequilibrium critical phenomena; however, its relation to the equilibrium quantum phase transition (EQPT) remains obscure. Substantial evidence has suggested that quenching across the underlying equilibrium phase boundary is neither a sufficient nor a necessary condition for the existence of the DQPT. In this work, we give a necessary and sufficient condition for the occurrence of DQPTs in two-band systems by introducing the quench fidelity, which is defined as the fidelity between the ground-state wave functions of the prequench and postquench Hamiltonian, and elaborate it by taking the one-dimensional anisotropic XY model as an example. The relation between EQPTs and DQPTs is analyzed in detail in terms of the quench fidelity.