Spatiotemporal scales of dynamical quantum phase transitions in the Bose-Hubbard model

TL;DR

This paper studies the spatial and temporal characteristics of dynamical quantum phase transitions in the one-dimensional Bose-Hubbard model, revealing how subsystem size influences the detection of these transitions.

Contribution

It introduces a systematic analysis of subsystem Loschmidt echo in the Bose-Hubbard model, identifying critical subsystem sizes and resolutions for observing quantum phase transitions.

Findings

Subsystem Loschmidt echo diverges logarithmically for large subsystems.

Critical exponent of the divergence is zero.

Guidelines for experimental detection of dynamical quantum phase transitions.

Abstract

We investigate the spatial and temporal scales of dynamical quantum phase transitions in the one-dimensional Bose-Hubbard model in the strong interaction limit. Using Jordan-Wigner transformation, we obtain the time-dependent wavefunction and therefore the subsystem Loschmidt echo, and systematically investigate how its properties vary with subsystem size. It is found that when the subsystem is sufficiently large, it exhibits logarithmic divergence identical to that of the full system Loschmidt echo, yielding a critical exponent of zero. We also obtain the required subsystem size and temporal resolution for detecting dynamical quantum phase transitions using the subsystem Loschmidt echo. It is expected that the present results provide a reliable foundation for further experimental investigations.