Fidelity approach to Gaussian transitions

TL;DR

This paper investigates the effectiveness of the fidelity susceptibility method in detecting Gaussian quantum phase transitions in spin-one XXZ chains, revealing its limitations for certain anisotropy parameters.

Contribution

The study applies the fidelity approach using DMRG to analyze Gaussian transitions in spin chains, highlighting its failure in specific cases and thus clarifying its applicability.

Findings

Fidelity susceptibility detects transitions at lambda=2.59 and 1.

Fails to detect transition at lambda=0.5.

Demonstrates limitations of the fidelity approach in quantum phase transition analysis.

Abstract

The fidelity approach to the Gaussian transitions in spin-one XXZ spin chains with three different values of Ising-like anisotropy lambda is analyzed by means of the density matrix renormalization group (DMRG) technique for systems of large sizes. We find that, despite the success in the cases of lambda=2.59 and 1, the fidelity susceptibility fails to detect the Gaussian transition for lambda=0.5. Thus our results demonstrate the limitation of the fidelity susceptibility in characterizing quantum phase transitions, which was proposed recently in general frameworks.