Re-Structuring Method for the Negative Sign Problem in Quantum Spin Systems

TL;DR

This paper introduces a re-structuring method that significantly alleviates the negative sign problem in quantum spin systems, demonstrated through exact diagonalization and transfer matrix analyses on small chains.

Contribution

The paper details a novel re-structuring approach for the path integral formulation that improves numerical stability in quantum spin system simulations.

Findings

Remarkable improvement in the negative sign problem for 1D quantum spin 1/2 systems.

Effective application of the method demonstrated through exact diagonalization.

Validation of the method's effectiveness via transfer matrix analysis.

Abstract

We present detailed discussions on a new approach we proposed in a previous paper to numerically study quantum spin systems. This method, which we will call re-structuring method hereafter, is based on rearrangement of intermediate states in the path integral formulation. We observed our approach brings remarkable improvement in the negative sign problem when applied to one-dimensional quantum spin $1/2$ system with next-to-nearest neighbor interactions. In this paper we add some descriptions on our method and show results from analyses by the exact diagonalization and by the transfer matrix method of the system on a small chain. These results also indicate that our method works quite effectively.