Exact numerical simulations of a one-dimensional, trapped Bose gas

TL;DR

This paper uses numerical density matrix renormalization group simulations to analyze the ground-state and low-temperature properties of a one-dimensional trapped Bose gas across different interaction regimes, confirming analytic predictions and characterizing correlation behaviors.

Contribution

It provides a comprehensive numerical study of a 1D trapped Bose gas from weak to strong interactions, validating local density approximation predictions and detailing correlation decay.

Findings

Agreement of local quantities with analytic predictions

Identification of temperature to quantum dominated correlation transition

Observation of algebraic decay of correlations in a harmonic trap

Abstract

We analyze the ground-state and low-temperature properties of a one-dimensional Bose gas in a harmonic trapping potential using the numerical density matrix renormalization group. Calculations cover the whole range from the Bogoliubov limit of weak interactions to the Tonks-Girardeau limit. Local quantities such as density and local three-body correlations are calculated and shown to agree very well with analytic predictions within a local density approximation. The transition between temperature dominated to quantum dominated correlation is determined and it is shown that despite the presence of the harmonic trapping potential first-order correlations display over a large range the algebraic decay of a harmonic fluid with a Luttinger parameter determined by the density at the trap center.