Partial-state fidelity and quantum phase transitions induced by continuous level crossing

TL;DR

This paper introduces partial-state fidelity as a tool to detect quantum phase transitions caused by continuous level crossing, overcoming limitations of global-state fidelity, and analyzes its scaling behavior in specific models.

Contribution

It proposes the use of partial-state fidelity and fidelity susceptibility to characterize level-crossing quantum phase transitions, with detailed scaling analysis in the LMG and Heisenberg models.

Findings

Partial-state fidelity signals level-crossing QPTs.

Fidelity susceptibility scales as N in LMG model.

Fidelity susceptibility scales as N^3 in Heisenberg model.

Abstract

The global-state fidelity cannot characterize those quantum phase transitions (QPTs) induced by continuous level crossing due to its collapse around each crossing point. In this paper, we take the isotropic Lipkin-Meshkov-Glick (LMG) model and the antiferromagnetic one-dimensional Heisenberg model as examples to show that the partial-state fidelity can signal such level-crossing QPTs. Extending to the thermodynamic limit we introduce the partial-state fidelity susceptibility and study its scaling behavior. The maximum of the partial-state fidelity susceptibility goes like $N$ for the LMG model and $N^3$ for the Heisenberg model.