Field Theoretic Simulations of a Finite Temperature Stripe Phase Found in Spin-orbit Coupled Bosons

We investigate the finite-temperature properties of interacting bosons endowed with an artificial spin-orbit coupling (SOC) in two dimensions. Using complex Langevin sampling of coherent states fields representing each hyperfine state, we access the equilibrium properties of spin-orbit coupled, pseudo-spin 1/2 bosons without approximation, despite the presence of a sign problem inherent to the SOC boson model. The Hamiltonian of interest admits two non-trivial BEC phases at the mean-field level — a stripe and plane-wave phase — due to the presence of degenerate single-particle ground states at non-zero momenta. This talk focuses on the stripe phase with smectic character and details the impact of thermal fluctuations on its characteristic pseudo-spin and momentum-space ordering. Furthermore, phase transitions are discussed in the context of weak crystallization Brazovskii theory as well as Berezinski-Kosterlitz-Thouless transitions characteristic of two-dimensional Bose gases.