Reduced fidelity susceptibility in the one-dimensional transverse field Ising model

TL;DR

This paper investigates the critical behavior of reduced fidelity susceptibility in the 1D transverse field Ising model, revealing a unique logarithmic divergence and providing analytical and numerical scaling analysis.

Contribution

It introduces the analysis of reduced fidelity susceptibility divergence, contrasting it with global fidelity, and derives its scaling behavior analytically and numerically.

Findings

Reduced fidelity susceptibility diverges as the square of logarithm.

The square root of susceptibility follows a power-law scaling.

Analytical and numerical results confirm the scaling exponent.

Abstract

We study critical behaviors of the reduced fidelity susceptibility for two neighboring sites in the one-dimensional transverse field Ising model. It is found that the divergent behaviors of the susceptibility take the form of square of logarithm, in contrast with the global ground-state fidelity susceptibility which is power divergence. In order to perform a scaling analysis, we take the square root of the susceptibility and determine the scaling exponent analytically and the result is further confirmed by numerical calculations.