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arXiv · 0907.0085

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

Jian Ma·Xiaoguang Wang·Shi-Jian Gu
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Abstract

We study the reduced fidelity susceptibility $χ_{r}$ for an $M$-body subsystem of an $N$-body Lipkin-Meshkov-Glick model with $τ=M/N$ 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 $χ_{r}$ behaves similar with the global fidelity susceptibility $χ_{g}$, the ratio $η=χ_{r}/χ_{g}$ depends on $τ$ but not $N$. However, at the critical point, the inner correlation tends to be divergent, then we find $χ_{r}$ approaches $χ_{g}$ with the increasing the $N$, and $η=1$ in the thermodynamic limit. The analytical predictions are perfect agreement with the numerical results.

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Jian Ma, Xiaoguang Wang, Shi-Jian Gu. 2009-07-01. Many-body reduced fidelity susceptibility in Lipkin-Meshkov-Glick model. https://doi.org/10.1103/physreve.80.021124

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