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Harmonically trapped ultra-cold atoms and helium-4 in nanopores provide newexperimental realizations of bosons in one dimension, motivating the search fora more complete theoretical understanding of their low energy properties. Wormalgorithm path integral quantum Monte Carlo results for interacting bosonsrestricted to the one dimensional continuum are compared to the finitetemperature and system size predictions of Luttinger liquid theory. For largesystem sizes at low temperature, excellent agreement is obtained afterincluding the leading irrelevant interactions in the Hamiltonian which aredetermined explicitly.

Interacting bosons in one dimension and Luttinger liquid theory