Entanglement entropy in the Lipkin-Meshkov-Glick model

We analyze the entanglement entropy in the Lipkin-Meshkov-Glick model, which describes mutually interacting spin 1/2 embedded in a magnetic field. This entropy displays a singularity at the critical point that we study as a function of the interaction anisotropy, the magnetic field, and the system size. Results emerging from our analysis are surprisingly similar to those found for the one- dimensional $XY$ chain.

Figure 1

Entanglement entropy for $N=500$ and $L=125$ as a function of $h$ and $\gamma$.

Figure 2

Entanglement entropy at $\gamma =0$ as a function of $h$ for different values of $N$ and $L$. Outside of the critical region, the entropy only depends on the ratio $L∕N$.

Figure 3

Entanglement entropy as a function of $h$ near the critical point for $\gamma =0$. The solid line corresponds to the fitting law (10) with $a=1∕6$.

Figure 4

Entanglement entropy as a function of $L$ at the critical point for different $\gamma$ and $N=2000$. The solid line corresponds to the fitting law (11) with $b=1∕3$.

Figure 5

Entanglement entropy at the critical point $h=1$ as a function of $\gamma$. The solid line corresponds to the fitting law (12) with $d=1∕6$.