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

TL;DR

This paper introduces numerical stabilization techniques for auxiliary field quantum Monte Carlo methods, enabling more accurate entanglement entropy calculations in large interacting fermion systems.

Contribution

It presents algorithmic improvements that mitigate numerical instabilities, allowing entanglement measures to be computed in larger systems within the DQMC framework.

Findings

Enhanced stability in entanglement entropy calculations

Application to quantum phase transition in Hubbard model

Comparable system sizes to conventional observable computations

Abstract

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