Complex wave fields in the interacting one-dimensional Bose gas

TL;DR

This paper evaluates the accuracy of the matter wave theory in 1D interacting Bose gases across temperature regimes by comparing it to the exact Yang-Yang solution, and determines optimal cutoff parameters for improved modeling.

Contribution

It introduces a method to assess the validity of the c-field theory in 1D Bose gases and identifies a universal cutoff that maximizes accuracy across various conditions.

Findings

Optimal cutoff is temperature-dependent but density and interaction independent.

High cutoff values are necessary for accurate kinetic energy predictions.

The approach provides bounds on accuracy for multiple observables.

Abstract

We study the temperature regimes of the 1d interacting gas to determine when the matter wave (c-field) theory is, in fact, correct and usable. The judgment is made by investigating the level of discrepancy in many observables at once in comparison to the exact Yang-Yang theory. We also determine what cutoff maximizes the accuracy of such an approach. Results are given in terms of a bound on accuracy, as well as an optimal cutoff prescription. For a wide range of temperatures the optimal cutoff is independent of density or interaction strength and so its temperature dependent form is suitable for many cloud shapes and, possibly, basis choices. However, this best global choice is higher in energy than most prior determinations. The high value is needed to obtain the correct kinetic energy, but does not detrimentally affect other observables.