Generalized fidelity susceptibility at phase transitions

TL;DR

This paper explores the relationship between quantum fidelity susceptibility and dynamical structure factors, introduces generalized fidelity susceptibility, and demonstrates its effectiveness in detecting certain quantum phase transitions.

Contribution

It provides a non-perturbative proof of QFS, relates it to dynamical structure factors, and extends the concept to generalized fidelity susceptibility for broader phase transition detection.

Findings

QFS is the negative-two-power moment of the dynamical structure factor.

GFS can detect criticalities where QFS fails, such as in fourth-order phase transitions.

The paper establishes a fundamental relation between physical quantities in linear response theory.

Abstract

In the present work, we investigate the intrinsic relation between quantum fidelity susceptibility (QFS) and the dynamical structure factor. We give a concise proof of the QFS beyond the perturbation theory. With the QFS in the Lehmann representation, we point out that the QFS actually the negative-two-power moment of dynamical structure factor, and illuminate the inherent relation between physical quantities in the linear response theory. Moreover, we discuss the generalized fidelity susceptibility (GFS) of any quantum relevant operator, that may not be coupled to the driving parameter, present similar scaling behaviors. Finally, we demonstrate that the QFS can not capture the fourth-order quantum phase transition in a spin-1/2 anisotropic XY chain in the transverse alternating field, while a lower-order GFS can seize the criticalities.