Influences of weak disorder on dynamical quantum phase transitions of anisotropic XY chain

TL;DR

This study investigates how weak and strong disorder influence dynamical quantum phase transitions in the anisotropic XY chain, revealing the emergence of new critical points and regions depending on disorder strength and quench parameters.

Contribution

The paper introduces a numerical method for calculating Loschmidt echo in disordered inhomogeneous systems and demonstrates how disorder modifies DQPTs in the XY chain.

Findings

Weak disorder induces new critical points during quenches crossing the Ising transition.

Increasing disorder broadens critical regions near the anisotropic transition.

Large disorder can suppress DQPTs in the paramagnetic phase.

Abstract

In this paper, the effects of disorder on the dynamical quantum phase transitions (DQPTs) in the transverse-field anisotropic XY chain are studied by numerically calculating the Loschmidt echo after quench. We obtain the formula for calculating the Loschmidt echo of the inhomogeneous system in real space. By comparing the results with that of the homogeneous chain, we find that when the quench crosses the Ising transition, the small disorder will cause a new critical point. As the disorder increases, more critical points of the DQPTs will occur, constituting a critical region. In the quench across the anisotropic transition, the disorder will cause a critical region near the critical point, and the width of the critical region increases by the disordered strength. In the case of quench passing through two critical lines, the small disorder leads to the system to have three additional critical points. When the quench is in the ferromagnetic phase, the large disorder causes the two critical points of the homogeneous case to become a critical region. And for the quench in the paramagnetic phase, the DQPTs will disappear for large disorder.