Multipartite entanglement and quantum criticality of Rydberg atoms trapped in a two-dimensional optical lattice

We investigate the multipartite entanglement and quantum criticality of neutral atoms on a two-dimensional square lattice, interacting via laser excitation to atom Rydberg states. It is found that the first derivative of residual entanglement with respect to detuning has peaks near the critical point, and corresponding critical behaviors are shown to obey conventional finite-sized scaling, from which we numerically determine the quantum critical point and the critical exponent of the associated correlation length. We also show that there is a sharp peak in the fidelity susceptibility near the critical point, and the critical exponent of the associated correlation length is obtained based on the finite size analysis.