Criticalities of the transverse- and longitudinal-field fidelity susceptibilities for the d=2 quantum Ising model

TL;DR

This study investigates the critical behaviors of fidelity susceptibilities in the 2D quantum Ising model, estimating critical exponents and confirming their independence and relation to conventional critical indices.

Contribution

It provides new numerical estimates of the critical exponents for both transverse- and longitudinal-field fidelity susceptibilities in the 2D quantum Ising model.

Findings

Critical exponent for transverse-field fidelity susceptibility: 0.752(24)

Critical exponent for longitudinal-field fidelity susceptibility: 1.81(13)

Fidelity susceptibility exponents are independent and relate to standard critical indices.

Abstract

The inner product between the ground-state eigenvectors with proximate interaction parameters, namely, the fidelity, plays a significant role in the quantum dynamics. In this paper, the critical behaviors of the transverse- and longitudinal-field fidelity susceptibilities for the d=2 quantum (transverse-field) Ising model are investigated by means of the numerical diagonalization method; the former susceptibility has been investigated rather extensively. The critical exponents for these fidelity susceptibilities are estimated as \alpha^{(t)}_F=0.752(24) and \alpha^{(h)}_F=1.81(13), respectively. These indices are independent, and suffice for obtaining conventional critical indices such as \nu=0.624(12) and \gamma=1.19(13).