Fisher information and spin squeezing in the Lipkin-Meshkov-Glick Model

TL;DR

This paper investigates how Fisher information can characterize quantum phase transitions in the Lipkin-Meshkov-Glick model, revealing enhanced parameter sensitivity in the broken phase and its potential as a diagnostic tool.

Contribution

It demonstrates the use of Fisher information to distinguish phases and identify quantum phase transitions in the Lipkin-Meshkov-Glick model.

Findings

Fisher information reaches the Heisenberg limit in the broken phase.

Parameter sensitivity is around the shot-noise limit in the symmetric phase.

Fisher information can serve as an indicator of quantum phase transitions.

Abstract

Fisher information, lies at the heart of parameter estimation theory, was recently found to have a close relation with multipartite entanglement (Pezz\'{e} and Smerzi, Phys. Rev. Lett. 102, 100401). We use Fisher information to distinguish and characterize behaviors of ground state of the Lipkin-Meskhov-Glick model, which displays a second-order quantum phase transition between the broken and symmetric phases. We find that the parameter sensitivity of the system attains the Heisenberg limit in the broken phase, while it is just around the shot-noise limit in the symmetric phase. Based on parameter estimation, Fisher information provides us an approach to the quantum phase transition.