Many-body localization transition through pairwise correlations

We investigate the phenomenon of spatial many-body localization (MBL) through pairwise correlation measures based on one-and two-point correlation functions. The system considered is the Heisenberg spin-1/2 chain with exchange interaction J and random on-site disorder of strength h. As a representative pairwise correlation measure obtained from one-point functions, we use global entanglement. Through its finite-size-scaling analysis, we locate the MBL critical point at hc/J = 3.8. As for measures involving two-point functions, we analyze pairwise geometric classical, quantum, and total correlations. Similarly to what happens for continuous quantum phase transitions, it is the derivatives of these two-point correlation measures that identify the MBL critical point, which is found to be in the range hc/J. [3,4]. Our approach relies on very simple measures that do not require access to multipartite entanglement or large portions of the system.