Loschmidt amplitude spectrum in dynamical quantum phase transitions

TL;DR

This paper introduces the Loschmidt amplitude spectrum (LAS) to analyze dynamical quantum phase transitions, revealing population redistribution in momentum space and connections to magnetization dynamics in both integrable and non-integrable models.

Contribution

The paper proposes the LAS as a new tool to study DQPTs, extending the traditional Loschmidt amplitude and applying it to both integrable and non-integrable quantum models.

Findings

LAS reveals population redistribution across DQPT in momentum space.

At DQPT, all lower-half k modes are excited in the quasiparticle picture.

System's magnetization dynamics are linked to LAS and eigenstate overlaps.

Abstract

Dynamical quantum phase transitions (DQPTs) are criticalities in the time evolution of quantum systems and their existence has been theoretically predicted and experimentally observed. However, how the system behaves in the vicinity of DQPT and its connection to physical observables remains an open question. In this work, we introduce the concept of the Loschmidt amplitude spectrum (LAS), which extends the Loscmidt amplitude - the detector of the transition - by considering the overlap of the initial state to all the eigenstates of the prequench Hamiltonian. By analysing the LAS in the integrable transverse-field Ising model, we find that the system undergoes a population redistribution in the momentum space across DQPT. In the quasiparticle picture, all the lower-half k modes are excited when the system is at DQPT. The LAS is also applicable to study the dynamics of non-integrable models where we have investigated the Ising model with next-nearest-neighbour interactions as an example. The time evolution of the system's magnetization is found to be connected to the products of the LAS and there exists a simultaneous overlap of the time-evolved state to pairs of eigenstates of the prequnech Hamiltonian that possess spin configurations of negative magnetization. Our findings provide a better understanding of the characteristics of the out-of-equilibrium system around DQPT.