Complex Langevin approach to interacting Bose gases

TL;DR

This paper investigates the use of the complex Langevin algorithm to simulate interacting Bose gases, demonstrating its effectiveness in calculating observables and critical temperature shifts in regimes relevant to experiments.

Contribution

It pioneers the application of the complex Langevin method to ultracold Bose gases, providing a new numerical tool for studying these systems beyond traditional techniques.

Findings

The CL method reliably computes observables in Bose gases.

Quantum corrections near the phase transition are captured, including critical temperature shifts.

The approach is promising for simulating realistic experimental setups.

Abstract

Quantitative numerical analyses of interacting dilute Bose-Einstein condensates are most often based on semi-classical approximations. Since the complex-valued field-theoretic action of the Bose gas does not offer itself to the direct application of standard Monte Carlo techniques, simulations beyond their scope by now almost exclusively rely on quantum-mechanical techniques. Here we explore an alternative approach based on a Langevin-type sampling in an extended state space, known as complex Langevin (CL) algorithm. While the use of the CL technique has a long-standing history in high-energy physics, in particular in the simulation of QCD at finitebaryon density, applications to ultracold atoms are still in their infancy. Here we examine the applicability of the CL approach for a one- and two-component, three-dimensional non-relativistic Bose gas in thermal equilibrium, below and above the Bose-Einstein phase transition. By comparison with analytic descriptions at the Gaussian level, including Bogoliubov and Hartree-Fock theory, we find that the method allows computing reliably and efficiently observables in the regime of experimentally accessible parameters. Close to the transition, quantum corrections lead to a shift of the critical temperature which we reproduce within the numerical range known in the literature. With this work, we aim to provide a first test of CL as a potential out-of-the-box tool for the simulation of experimentally realistic situations, including trapping geometries and multicomponent/-species models.