Entanglement and the fermion sign problem in auxiliary field quantum Monte Carlo simulations

TL;DR

This paper explores how entanglement measures, especially Renyi entropies, can mitigate the fermion sign problem in auxiliary-field quantum Monte Carlo simulations, enabling the study of larger fermionic systems despite exponential sampling errors.

Contribution

It demonstrates that entanglement measures can be robust against the sign problem, allowing for the analysis of global ground-state properties in strongly sign-problematic fermionic systems.

Findings

Entanglement measures show robustness against the sign problem.

Scaling of Renyi entropies reveals ground-state properties.

Numerical simulations confirm the approach in fermionic phase transitions.

Abstract

Quantum Monte Carlo simulations of fermions are hampered by the notorious sign problem whose most striking manifestation is an exponential growth of sampling errors with the number of particles. With the sign problem known to be an NP-hard problem and any generic solution thus highly elusive, the Monte Carlo sampling of interacting many-fermion systems is commonly thought to be restricted to a small class of model systems for which a sign-free basis has been identified. Here we demonstrate that entanglement measures, in particular the so-called Renyi entropies, can intrinsically exhibit a certain robustness against the sign problem in auxiliary-field quantum Monte Carlo approaches and possibly allow for the identification of global ground-state properties via their scaling behavior even in the presence of a strong sign problem. We corroborate these findings via numerical simulations of fermionic quantum phase transitions of spinless fermions on the honeycomb lattice at and below half-filling.