Critical behavior of the fidelity susceptibility for the d=2 transverse-field Ising model

TL;DR

This study investigates the critical behavior of fidelity susceptibility in the 2D transverse-field Ising model using numerical diagonalization, revealing a specific critical exponent and advantages of the method in reducing finite-size artifacts.

Contribution

It provides the first detailed numerical analysis of fidelity susceptibility critical behavior in the 2D transverse-field Ising model, including an estimate of the critical exponent.

Findings

Fidelity susceptibility critical exponent estimated as 0.715(20).

Finite-size artifacts are suppressed compared to Binder parameter.

Numerical diagonalization with screw-boundary condition effectively analyzes critical behavior.

Abstract

The overlap (inner product) between the ground-state eigenvectors with proximate interaction parameters, the so-called fidelity, plays a significant role in the quantum-information theory. In this paper, the critical behavior of the fidelity susceptibility is investigated for the two-dimensional tranverse-field (quantum) Ising model by means of the numerical diagonalization method. In order to treat a variety of system sizes N=12,14,...,32, we adopt the screw-boundary condition. Finite-size artifacts (scaling corrections) of the fidelity susceptibility appear to be suppressed, as compared to those of the Binder parameter. As a result, we estimate the fidelity-susceptibility critical exponent as \alpha_F =0.715(20).