Stochastic Simulation of a finite-temperature one-dimensional Bose-Gas: from Bogoliubov to Tonks-Girardeau regime

TL;DR

This paper introduces a stochastic computational method to accurately calculate the thermal properties of a 1D Bose-gas across different interaction regimes, from weak to strong, including quantum fluctuation effects.

Contribution

It develops a novel stochastic approach with block factorization and DMRG ideas to simulate the entire interaction range of a 1D Bose-gas at finite temperatures.

Findings

Agreement with analytic predictions for density and correlations

Effective simulation of quantum fluctuations at low temperatures

Method applicable across weak to strong interaction regimes

Abstract

We present an ab initio stochastic method for calculating thermal properties of a trapped, 1D Bose-gas covering the whole range from weak to strong interactions. Discretization of the problem results in a Bose-Hubbard-like Hamiltonian, whose imaginary time evolution is made computationally accessible by stochastic factorization of the kinetic energy. To achieve convergence for low enough temperatures such that quantum fluctuations are essential, the stochastic factorization is generalized to blocks, and ideas from density-matrix renormalization are employed. We compare our numerical results for density and first-order correlations with analytic predictions.