Interacting bosons in one dimension and the applicability of Luttinger-liquid theory as revealed by path-integral quantum Monte Carlo calculations

Abstract

Harmonically trapped ultracold atoms and $^{4}\text{H}\text{e}$ in nanopores provide different 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.