Mitigating the fermion sign problem by automatic differentiation

TL;DR

This paper introduces ADSO, a novel automatic differentiation-based framework that optimizes quantum Monte Carlo schemes, effectively mitigating the sign problem and enabling accurate simulations of complex quantum systems.

Contribution

The paper presents a general framework using automatic differentiation to find optimal QMC schemes, successfully mitigating the sign problem in the Hubbard model.

Findings

Discovered a sign-free point in the Hubbard model with Rashba coupling.

Demonstrated the effectiveness of ADSO in mitigating the sign problem.

Characterized the magnetic quantum phase transition in the sign-free model.

Abstract

As an intrinsically unbiased method, the quantum Monte Carlo (QMC) method is of unique importance in simulating interacting quantum systems. Although the QMC method often suffers from the notorious sign problem, the sign problem of quantum models may be mitigated by finding better choices of the simulation scheme. However, a general framework for identifying optimal QMC schemes has been lacking. Here, we propose a general framework using automatic differentiation to automatically search for the best QMC scheme within a given ansatz of the Hubbard-Stratonovich transformation, which we call "automatic differentiable sign optimization" (ADSO). We apply the ADSO framework to the honeycomb lattice Hubbard model with Rashba spin-orbit coupling and demonstrate that ADSO is remarkably effective in mitigating and even solving its sign problem. Specifically, ADSO finds a sign-free point in the model which was previously thought to be sign-problematic. For the sign-free model discovered by ADSO, its ground state is shown by sign-free QMC simulations to possess spiral magnetic ordering; we also obtained the critical exponents characterizing the magnetic quantum phase transition.