Exotic signature of dynamical quantum phase transition in the time evolution of engineered initial state

TL;DR

This paper explores dynamical quantum phase transitions in a quantum Ising chain starting from generic initial states, revealing both phase-transition-related and unrelated non-analytic behaviors in the rate function during time evolution.

Contribution

It demonstrates that non-analyticities in the Loschmidt echo can occur without an equilibrium phase transition, depending on the initial state configuration.

Findings

Certain singularities relate to the quantum critical point.

Some non-analyticities occur independently of equilibrium transitions.

Quasiparticle occupancy influences the emergence of non-analyticities.

Abstract

Dynamical phase transition in quantum many body systems is usually studied by taking it in the ground state and then quenching a parameter to a new value. We investigate here the dynamics when one performs the time evolution of a generic state and observe that the rate function related to the Loschmidt echo shows non-analytic behavior of two types, one related, and the other unrelated, to the appearance of a quantum phase transition. Specifically, we consider a quantum Ising chain in an initial configuration which is a generic superposition of the eigenstates, and follow its dynamics under the transverse Ising Hamiltonian with constant field. Depending on the the configuration of the initial state, some singularities appear in the rate function which do not correspond to the equilibrium phase transition of the Hamiltonian. However another class of singularity is found having connection with the quantum critical point. Some features of the singularities of the rate function have been derived analytically and it is observed that the occupancy of quasiparticle eigenstates plays the key role in triggering the non-analyticities.