Simulation of ultracold Bose gases with the complex Langevin method

TL;DR

This thesis explores the use of the complex Langevin algorithm to perform numerically exact lattice Monte Carlo simulations of ultracold Bose gases, overcoming the complex action problem inherent in traditional methods.

Contribution

It provides a comprehensive framework for simulating interacting Bose-Einstein condensates using the complex Langevin method, including new results for trapped and dipolar gases.

Findings

Successful simulation of 3D and 2D homogeneous Bose gases

Extension to systems with external trapping potentials

Inclusion of long-range dipolar interactions

Abstract

This PhD thesis gives a comprehensive treatment of ab initio lattice Monte Carlo simulations of ultracold Bose gases by means of the complex Langevin algorithm. Since the field-theoretic action of non-relativistic bosons is a complex quantity, the corresponding path integral features a complex weight and is not accessible to standard Monte Carlo techniques. The complex Langevin algorithm represents an approach to overcome this obstacle, thereby providing the intriguing possibility of numerically exact simulations of interacting Bose-Einstein condensates within the field-theoretic framework. After reviewing the coherent-state path integral description of ultracold Bose gases as well as the complex Langevin method, we present the results of simulations in several physical scenarios. While parts of the thesis are based on arXiv:2204.10661 and arXiv:2304.05699 that treat the 3D and 2D homogeneous gas with contact interactions, it contains additional material covering external trapping potentials as well as Bose gases with long-range dipolar interactions.