Exact kinetic propagators for coherent state complex Langevin simulations

We introduce and benchmark an improved algorithm for complex Langevin simulations of bosonic coherent state path integrals in the preprint. Our approach utilizes a Strang splitting of the imaginary-time propagator rather than the conventional linear-order Taylor expansion, allowing us to construct an action that incorporates higher-order terms at negligible computational cost. The resulting algorithm enjoys guaranteed linear stability independent of the imaginary-time discretization, enabling more resource-efficient simulations. We demonstrate this improved performance for single-species bosons and for two-component bosons with Rashba spin-orbit coupling. The enclosed data set shows a method comparison between the standard "primitive" approach and the quadratic propagator technique used in this manuscript for many thermodynamic observables of interest.

Methods
Both methods involve complex Langevin sampling of a coherent state path integral, built from a second-quantized description of interacting bosons at finite temperature. Details are provided in the enclosed manuscript as well as the following publications: https://doi.org/10.1103/PhysRevLett.131.173403 and https://doi.org/10.1103/PhysRevLett.124.070601