Interacting bosons in one dimension and Luttinger liquid theory

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.