Scaling of the fidelity susceptibility in a disordered quantum spin chain

TL;DR

This study examines how disorder affects quantum phase transitions in a disordered XY spin chain by analyzing the fidelity susceptibility, revealing disorder-induced phases and scaling behaviors distinct from the clean system.

Contribution

It introduces a detailed finite-size scaling analysis of the fidelity susceptibility in a disordered quantum spin chain, highlighting disorder effects on criticality and Griffiths phases.

Findings

Disorder causes a disappearance of criticality and emergence of Griffiths phases.

Fidelity susceptibility is not self-averaging near critical lines.

Scaling of fidelity susceptibility differs from the disorder-free case, showing stretched exponential and extensive behaviors.

Abstract

The phase diagram of a quantum XY spin chain with Gaussian-distributed random anisotropies and transverse fields is investigated, with focus on the fidelity susceptibility, a recently introduced quantum information theoretical measure. Monitoring the finite-size scaling of the probability distribution of this quantity as well as its average and typical values, we detect a disorder-induced disappearance of criticality and the emergence of Griffiths phases in this model. It is found that the fidelity susceptibility is not self-averaging near the disorder-free quantum critical lines. At the Ising critical point the fidelity susceptibility scales as a disorder-strength independent stretched exponential of the system size, in contrast with the quadratic scaling at the corresponding point in the disorder-free XY chain. Along the line where the average anisotropy vanishes the fidelity susceptibility appears to scale extensively, whereas in the disorder-free case this point is quantum critical with quadratic finite-size scaling.