Quantum criticality of the Lipkin-Meshkov-Glick Model in terms of fidelity susceptibility

TL;DR

This paper analytically investigates the critical behavior of the Lipkin-Meshkov-Glick Model using fidelity susceptibility, revealing non-trivial critical exponents and insights into quantum phase transition universality.

Contribution

It provides the first explicit analytical derivation of the fidelity susceptibility's critical exponent in the LMG model, highlighting its non-extensive nature across phases.

Findings

Critical exponent of fidelity susceptibility derived analytically.

Fidelity susceptibility exhibits non-trivial critical behavior.

Different critical exponents in two phases indicate complex universality.

Abstract

We study the critical properties of the Lipkin-Meshkov-Glick Model in terms of the fidelity susceptibility. By using the Holstein-Primakoff transformation, we obtain explicitly the critical exponent of the fidelity susceptibility around the second-order quantum phase transition point. Our results provide a rare analytical case for the fidelity susceptibility in describing the universality class in quantum critical behavior. The different critical exponents in two phases are non-trivial results, indicating the fidelity susceptibility is not always extensive.