Determination of dynamical quantum phase transition for boson systems using the Loschmidt cumulants method

TL;DR

This paper investigates dynamical quantum phase transitions in the Bose-Hubbard model using Loschmidt cumulants, accurately identifying critical points and introducing energy fluctuation analysis as a new tool, including extended models.

Contribution

The study applies Loschmidt cumulants to determine DQPT critical points in Bose-Hubbard models with high accuracy and introduces energy fluctuation analysis as a novel method.

Findings

High-accuracy determination of DQPT critical points

Loschmidt zeros analogous to Lee-Yang zeros

Energy fluctuation analysis as a new tool

Abstract

We study the dynamical quantum phase transition(DQPT) of the Bose-Hubbard model utilizing recently developed Loschmidt cumulants method. We determine the complex Loschmidt zeros of the Loschmidt amplitude analogous to the Lee-Yang zeros of the thermal partition function. We obtain the DQPT critical points through identifying the crossing points with the imaginary axis. The critical points show high accuracy when compared to those obtained using the matrix product states method. In addition, we show that how the critical points of DQPT can be determined by analyzing the energy fluctuation of the initial state, making it a valuable tool for future studies in this area. Finally, DQPT in the extended Bose-Hubbaed model is also investigated.