Reduced fidelity susceptibility and its finite-size scaling behaviors

TL;DR

This paper derives a formula for reduced fidelity susceptibility in certain quantum states and demonstrates its effectiveness in characterizing quantum phase transitions using only subsystem information, with practical experimental implications.

Contribution

The paper introduces a general formula for reduced fidelity susceptibility in 2x2 block-diagonal states and applies it to analyze finite-size scaling in the Lipkin-Meshkov-Glick Model.

Findings

Reduced fidelity susceptibility can characterize quantum phase transitions.

Subsystem fidelity provides practical experimental insights.

Finite-size scaling behavior is elucidated in the model.

Abstract

We derive a general formula of the reduced fidelity susceptibility when the reduced density matrix is $2\times2$ block-diagonal. By using this result and the continuous unitary transformations, we study finite-size scaling of the reduced fidelity susceptibility in the Lipkin-Meshkov-Glick Model. It is found that it can be used to characterize quantum phase transitions, implying that we can extract information of quantum phase transitions only from the fidelity of a subsystem, which is of practical meaning in experiments.