Critical Exponent of Dynamical Quantum Phase Transition in One-Dimensional Bose-Hubbard Model in the Strong Interacting Limit

TL;DR

This paper analytically studies dynamical quantum phase transitions in the one-dimensional Bose-Hubbard model, revealing universal critical behavior characterized by cusp singularities and a zero critical exponent after a quench.

Contribution

It provides the first analytical demonstration of the critical exponent and universal cusp singularity in dynamical quantum phase transitions within the strongly interacting Bose-Hubbard model.

Findings

Loschmidt echo exhibits cusp singularities with logarithmic divergence.

Critical exponent of the transition is zero.

Modifying the harmonic potential controls transition timing.

Abstract

We analytically investigated the dynamical quantum phase transitions in the Bose-Hubbard model using the Loschmidt echo as an observable, revealing that after a quench, the global Loschmidt echo exhibits cusp singularities with a logarithmically divergent rate function near criticality and a critical exponent of zero. Through extensive calculations across various system sizes and initial states, we have demonstrated that in the strongly interacting regime, the critical singularity of dynamical quantum phase transitions exhibits consistency across different model details and initial product states (charge-density wave states). Moreover, we find that modifying the harmonic potential well not only preserves the phase transition but also enables precise control over the transition timing.