TY  - GEN
A1  - Heinen, Philipp
AV  - public
ID  - heidok34814
Y1  - 2024///
UR  - https://archiv.ub.uni-heidelberg.de/volltextserver/34814/
N2  - Evaluating the field-theoretic path integral of interacting non-relativistic bosons is not feasible with standard Monte Carlo techniques because the kinetic term in the action is purely imaginary, rendering the path integral weight a complex quantity. The complex Langevin (CL) method attempts to circumvent this problem by recasting the path integral into a stochastic differential equation and by complexifying originally real degrees of freedom. We explore the applicability of the algorithm in numerous scenarios and demonstrate that it is a viable tool for the numerically exact simulation of weakly interacting Bose gases. We first review the construction of the path integral of non-relativistic bosons and discuss in depth its discretization on a computational lattice as well as the extraction of observables; furthermore, the CL method is reviewed. We then perform benchmark studies of CL simulations against approximate analytical descriptions of the three-dimensional Bose gas in the condensed and thermal phase and against literature predictions for the critical temperature. In a two-dimensional gas, we study the Berezinskii-Kosterlitz-Thouless transition, recovering its known hallmarks and extracting the critical temperature. We also compute density profiles in a two-dimensional harmonic trap and compare them to experiment. Finally, we employ the CL method to simulate dipolar Bose gases. We consider both the stable phase above the roton instability, where we compare excitation energies to experiment, as well as the unstable one, where we demonstrate the stabilizing effect of quantum fluctuations.
CY  - Heidelberg
TI  - Simulation of ultracold Bose gases with the complex Langevin method
ER  -