We study the crossover of a finite one-dimensional bosonic ensemble from weak to strong interactions in harmonic traps and multi-well potentials. We perform diffusion quantum Monte Carlo calculations which we show to be in good agreement with results from analytical functions that we construct to describe these systems. For the harmonic trap, we use the correlated-pair wavefunction which we introduced in Brouzos and Schmelcher (2012 Phys. Rev. Lett. 108 045301) considering here much larger atom numbers, going beyond the few body ensembles studied in our previous work. We also investigate double and triple wells, changing correspondingly the uncorrelated part of the ansatz to describe efficiently the single-particle behaviour. On-site effects beyond mean-field and standard Bose–Hubbard calculations that appear in densities being captured by our analytical functions are explored.We study the crossover of a finite one-dimensional bosonic ensemble from weak to strong interactions in harmonic traps and multi-well potentials. We perform diffusion quantum Monte Carlo calculations which we show to be in good agreement with results from analytical functions that we construct to describe these systems. For the harmonic trap, we use the correlated-pair wavefunction which we introduced in Brouzos and Schmelcher (2012 Phys. Rev. Lett. 108 045301) considering here much larger atom numbers, going beyond the few body ensembles studied in our previous work. We also investigate double and triple wells, changing correspondingly the uncorrelated part of the ansatz to describe efficiently the single-particle behaviour. On-site effects beyond mean-field and standard Bose–Hubbard calculations that appear in densities being captured by our analytical functions are explored.

arXiv:1210.7769Journal of Physics B Atomic Molecular and Optical PhysicsJan 29, 20133 citations

Quantum Monte Carlo simulation of a two-dimensional Bose gas (5 pages)

Jordi Boronat, Sebastiano Pilati, J. Casulleras

Physical Review AJan 1, 20050 citations

Finite-temperature theory of the trapped two-dimensional Bose gas (4 pages)

Brandon P. van Zyl, Christopher Gies

Physical Review AJan 1, 20040 citations

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

Adrian Del Maestro, Ian K. Affleck

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.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.

arXiv:1005.5383Physical Review BAug 26, 201065 citations

Two-dimensional boson–fermion mixtures in harmonic traps

B. Tanatar, E. Erdemir

Physica B Condensed MatterMay 1, 20032 citations

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.