# Thermodynamics of spin-orbit coupled bosons in two dimensions from complex Langevin

## TL;DR

This paper uses the complex Langevin method to study the thermodynamics of two-dimensional spin-orbit coupled bosons, revealing limitations of mean-field theory and effects of spin-orbit interactions on pseudo-condensates.

## Contribution

It introduces a non-perturbative computational approach to analyze the thermodynamics of spin-orbit coupled bosons in two dimensions, addressing the sign problem.

## Key findings

- Mean-field solutions underestimate the density at strong spin-orbit coupling.
- Finite volume effects lead to pseudo-condensate formation.
- Spin-orbit interactions destroy pseudo-condensates.

## Abstract

We investigate the thermal properties of interacting spin-orbit coupled bosons with contact interactions in two spatial dimensions. To that end, we implement the complex Langevin method, motivated by the appearance of a sign problem, on a square lattice with periodic boundary conditions. We calculate the density equation of state non-perturbatively in a range of spin-orbit couplings and chemical potentials. Our results show that mean-field solutions tend to underestimate the average density, especially for stronger values of the spin-orbit coupling. Additionally, the finite nature of the simulation volume induces the formation of pseudo-condensates. These have been observed to be destroyed by the spin-orbit interactions.