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

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.

Complex Langevin simulations and the QCD phase diagram: recent developments

“…Additional uses of complex Langevin outside of QCD related models include superstring-inspired models [32] and quantum many-body studies: rotating bosons [33,34], spin-orbit coupled bosons [35], fermions with repulsive interactions [36], non-zero polarisation [37,38], mass imbalance [39,40], and to determine their virial coefficients [41].…”

Pairing patterns in polarized unitary Fermi gases above the superfluid transition

“…) is the effective action, and η represents a (real) white noise term with vanishing autocorrelation. Although there are potential caveats to this approach [34][35][36], this strategy has been successfully applied to strongly coupled ultracold matter [20,26,[37][38][39][40] and thus is expected to faithfully represent the correlation functions of interest for this work. Our numerical setup and (hyper)parameters are as in Ref.…”

A lattice pairing-field approach to ultracold Fermi gases

“…Such theories are known to have a sign problem on a spacetime lattice. In order to deal with this sign problem, we employ the complex Langevin (CL) approach, which has been employed before to study relativistic as well as non-relativistic complex scalar field theories [53][54][55]. Moreover, the CL approach has been successfully applied to compute properties of ultracold Fermi gases described by the Hamilton operator (1), see Refs.…”