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In the absence of a fermion sign problem, auxiliary field (or determinantal)quantum Monte Carlo (DQMC) approaches have long been the numerical method ofchoice for unbiased, large-scale simulations of interacting many-fermionsystems. More recently, the conceptual scope of this approach has been expandedby introducing ingenious schemes to compute entanglement entropies within itsframework. On a practical level, these approaches however suffer from a varietyof numerical instabilities that have largely impeded their applicability. Herewe report on a number of algorithmic advances to overcome many of thesenumerical instabilities and significantly improve the calculation ofentanglement measures in the zero-temperature projective DQMC approach,ultimately allowing to reach similar system sizes as for the computation ofconventional observables. We demonstrate the applicability of this improvedDQMC approach by providing an entanglement perspective on the quantum phasetransition from a magnetically ordered Mott insulator to a band insulator inthe bilayer square lattice Hubbard model at half filling.

Numerical stabilization of entanglement computation in auxiliary field quantum Monte Carlo simulations of interacting many-fermion systems