Correlation properties of a one-dimensional repulsive Bose gas at finite temperature

TL;DR

This paper uses exact Monte Carlo simulations to analyze how thermal fluctuations influence correlations in a one-dimensional repulsive Bose gas across different interaction strengths and temperatures, providing benchmarks for future experiments.

Contribution

It offers a comprehensive, ab-initio analysis of correlation functions in a 1D Bose gas at finite temperature, comparing multiple theoretical approaches with exact Monte Carlo results.

Findings

Excellent agreement with theoretical limits

Benchmark data for experimental platforms

Detailed analysis across interaction and temperature regimes

Abstract

We present a comprehensive study shedding light on how thermal fluctuations affect correlations in a Bose gas with contact repulsive interactions in one spatial dimension. The pair correlation function, the static structure factor, and the one-body density matrix are calculated as a function of the interaction strength and temperature with the exact ab-initio Path Integral Monte Carlo method. We explore all possible gas regimes from weak to strong interactions and from low to high temperatures. We provide a detailed comparison with a number of theories, such as perturbative (Bogoliubov and decoherent classical), effective (Luttinger liquid) and exact (ground-state and thermal Bethe Ansatz) ones. Our Monte Carlo results exhibit an excellent agreement with the tractable limits and provide a fundamental benchmark for future observations which can be achieved in atomic gases, cavity quantum-electrodynamic and superconducting-circuit platforms.