Local Basis Transformation to Mitigate Negative Sign Problems

TL;DR

This paper introduces a systematic method to reduce the negative sign problem in quantum Monte Carlo simulations by optimizing the basis representation, especially effective in frustration-free quantum spin systems.

Contribution

It proposes a basis optimization approach using a locally defined loss function to mitigate the sign problem, independent of the Hamiltonian or lattice structure.

Findings

Optimizing the basis reduces the severity of the sign problem in several models.

Unitary transformations can be more effective than orthogonal transformations in mitigating the sign problem.

The negativity measure helps characterize and address the sign problem severity.

Abstract

Quantum Monte Carlo (QMC) methods for the frustrated quantum spin systems occasionally suffer from the negative sign problem, which makes simulations exponentially harder for larger systems at lower temperatures and severely limits QMC's application across a wide range of spin systems. This problem is known to depend on the choice of representation basis. We propose a systematic approach for mitigating the sign problem independent of the given Hamiltonian or lattice structure. We first introduce the concept of negativity to characterize the severity of the negative sign problem. We then demonstrate the existence of a locally defined quantity, the L1 adaptive loss function, which effectively approximates negativity, especially in frustration-free systems. Using the proposed loss function, we demonstrate that optimizing the representation basis can mitigate the negative sign. This is evidenced by several frustration-free models and other important quantum spin systems. Furthermore, we compare the effectiveness of unitary transformations against the standard orthogonal transformation and reveal that unitary transformations can effectively mitigate the sign problem in certain cases.