Many-body reduced fidelity susceptibility in Lipkin-Meshkov-Glick model

TL;DR

This paper investigates how the reduced fidelity susceptibility of a subsystem in the Lipkin-Meshkov-Glick model behaves near criticality, revealing that it converges to the global susceptibility as system size grows.

Contribution

It provides analytical and numerical analysis of the reduced fidelity susceptibility in the LMG model, especially at the critical point, highlighting the relationship between subsystem and global responses.

Findings

Reduced fidelity susceptibility matches global susceptibility at criticality.

The ratio of reduced to global susceptibility depends on subsystem size away from criticality.

Analytical predictions agree with numerical simulations.

Abstract

We study the reduced fidelity susceptibility $\chi_{r}$ for an $M$-body subsystem of an $N$-body Lipkin-Meshkov-Glick model with $\tau=M/N$ fixed. The reduced fidelity susceptibility can be viewed as the response of subsystem to a certain parameter. In noncritical region, the inner correlation of the system is weak, and $\chi_{r}$ behaves similar with the global fidelity susceptibility $\chi_{g}$, the ratio $\eta=\chi_{r}/\chi_{g}$ depends on $\tau$ but not $N$. However, at the critical point, the inner correlation tends to be divergent, then we find $\chi_{r}$ approaches $\chi_{g}$ with the increasing the $N$, and $\eta=1$ in the thermodynamic limit. The analytical predictions are perfect agreement with the numerical results.