Interacting bosons in one dimension and Luttinger liquid theory

TL;DR

This paper compares quantum Monte Carlo simulations of one-dimensional interacting bosons with Luttinger liquid theory predictions, demonstrating excellent agreement at large sizes and low temperatures when including irrelevant interactions.

Contribution

It provides a detailed comparison between numerical simulations and Luttinger liquid theory, explicitly including leading irrelevant interactions for better accuracy.

Findings

Excellent agreement between QMC results and Luttinger liquid theory at large sizes and low temperatures.

Explicit determination and inclusion of leading irrelevant interactions improve theoretical predictions.

Validates Luttinger liquid theory as a reliable low-energy description for 1D bosonic systems.

Abstract

Harmonically trapped ultra-cold atoms and helium-4 in nanopores provide new experimental realizations of bosons in one dimension, motivating the search for a more complete theoretical understanding of their low energy properties. Worm algorithm path integral quantum Monte Carlo results for interacting bosons restricted to the one dimensional continuum are compared to the finite temperature and system size predictions of Luttinger liquid theory. For large system sizes at low temperature, excellent agreement is obtained after including the leading irrelevant interactions in the Hamiltonian which are determined explicitly.