Scaling Properties of Fidelity in Spin-one Anisotropic Model

TL;DR

This paper uses the density matrix renormalization group to verify the scaling of fidelity susceptibility in a spin-one XXZ chain, identifying critical points and exponents, thus supporting fidelity as a tool for quantum phase transition detection.

Contribution

It provides numerical validation of the fidelity susceptibility scaling relation and its effectiveness in detecting quantum phase transitions in spin chains.

Findings

Confirmed the scaling relation of fidelity susceptibility

Identified critical points and exponents consistent with literature

Supported fidelity's use in quantum phase transition detection

Abstract

By means of the density matrix renormalization group technique, the scaling relation of the fidelity susceptibility proposed recently is verified for the spin-one XXZ spin chain with an on-site anisotropic term. Moreover, from the results of both the fidelity susceptibility and the entanglement entropy, the critical points and some of the corresponding critical exponents are determined through a proper finite-size scaling analysis, and these values agree with the findings in the literature. Thus our work provides a numerical support of the use of the fidelity in detecting quantum phase transitions.