Diffusion Monte Carlo methods for Spin-Orbit-Coupled ultracold Bose gases

TL;DR

This paper introduces two novel Diffusion Monte Carlo algorithms tailored for ultracold quantum gases with spin-orbit interactions, enhancing accuracy and computational efficiency in simulating such complex systems.

Contribution

The paper develops and compares two new DMC algorithms for spin-orbit-coupled ultracold gases, one providing an upper bound and the other offering higher accuracy under certain conditions.

Findings

Both algorithms agree with other numerical methods.

The spin-integrated DMC is more accurate but limited to spin-independent interactions.

The discrete spin DMC provides an upper bound to the fixed-phase energy.

Abstract

We present two Diffusion Monte Carlo (DMC) algorithms for systems of ultracold quantum gases featuring synthetic spin-orbit interactions. The first one is a discrete spin generalization of the T- moves spin-orbit DMC, which provides an upper bound to the fixed-phase energy. The second is a spin-integrated DMC method which recovers the fixed-phase property by avoiding the definition of the effective Hamiltonian involved in the T-moves approach. The latter is a more accurate method but it is restricted to spin-independent two-body interactions. We report a comparison between both algorithms for different systems. As a check of the efficiency of both methods, we compare the DMC energies with results obtained with other numerical methods, finding agreement between both estimation