Auxiliary-Field Quantum Monte Carlo for Calculating the Renyi and Accessible Entanglement Entropies

In this work, we introduce an Auxiliary-Field Quantum Monte Carlo algorithm to measure the Renyi and accessible entanglement entropy (EE) for systems of interacting fermions in both the canonical and grand canonical ensembles. This approach generalizes a recursive method we recently developed for performing AFQMC in the canonical ensemble to enable replica sampling for systems and subsystems with a fixed particle number, which allows for the measurement of the Renyi and particle-number-resolved accessible EEs. We present comparisons of the EEs in the two different ensembles as a function of the interaction strength and temperature to illustrate how the entanglements can be affected by explicit particle number constraints. Furthermore, we demonstrate how the EEs can be used as accurate probes of first-order phase transitions.