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We investigate the thermal properties of interacting spin-orbit coupledbosons with contact interactions in two spatial dimensions. To that end, weimplement the complex Langevin method, motivated by the appearance of a signproblem, on a square lattice with periodic boundary conditions. We calculatethe density equation of state non-perturbatively in a range of spin-orbitcouplings and chemical potentials. Our results show that mean-field solutionstend to underestimate the average density, especially for stronger values ofthe spin-orbit coupling. Additionally, the finite nature of the simulationvolume induces the formation of pseudo-condensates. These have been observed tobe destroyed by the spin-orbit interactions.

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