Adaptive Sampling Approach to the Negative Sign Problem in the Auxiliary Field Quantum Monte Carlo Method

TL;DR

The paper introduces the adaptive sampling quantum Monte Carlo (ASQMC) method, which reduces the negative sign problem in auxiliary field quantum Monte Carlo calculations, achieving accurate results without constraints.

Contribution

The novel ASQMC method utilizes high temperature density matrix information to significantly mitigate the negative sign problem in quantum Monte Carlo simulations.

Findings

Negative sign ratio is greatly reduced with ASQMC.

The sign ratio approaches zero as $ riangle au$ approaches zero.

ASQMC provides accurate results across various physical parameters.

Abstract

We propose a new sampling method to calculate the ground state of interacting quantum systems. This method, which we call the adaptive sampling quantum monte carlo (ASQMC) method utilises information from the high temperature density matrix derived from the monte carlo steps. With the ASQMC method, the negative sign ratio is greatly reduced and it becomes zero in the limit $\Delta \tau$ goes to zero even without imposing any constraint such like the constraint path (CP) condition. Comparisons with numerical results obtained by using other methods are made and we find the ASQMC method gives accurate results over wide regions of physical parameters values.