Bosons confined in optical lattices: The numerical renormalization group revisited

Abstract

A Bose-Hubbard model, describing bosons in a harmonic trap with a superimposed optical lattice, is studied using a fast and accurate variational technique (MFϩNRG): the Gutzwiller mean-field (MF) ansatz is combined with a numerical renormalization group (NRG) procedure in order to improve on both. Results are presented for one, two, and three dimensions, with particular attention to the experimentally accessible momentum distribution and possible satellite peaks in this distribution. In one dimension, a comparison is made with exact results obtained using stochastic series expansion.

Hyperfine spectra of trapped bosons in optical lattices

“…This approach is exact in infinite dimensions and in the deep Mott insulator and superfluid limits. Sophisticated numerical calculations, some with a trapping potential, have shown that this mean field theory yields qualitatively accurate phase diagrams, energies, and spatial density profiles [14,15,16,17,18]. As a point of reference, Monte-Carlo calculations predict that for unity filling the 3D Bose-Hubbard model on a cubic lattice has an insulator-superfluid transition at t/U = 0.03408(2), while mean field theory gives t/U = 0.029.…”

Interplay between temperature and trap effects in one-dimensional lattice systems of bosonic particles

“…[7,10,[14][15][16][17][18][19][20][21][22][23]). However, at fixed trap size, the system does not develop a critical behavior with a diverging length scale [14,18].…”

Ultracold Atoms in One-Dimensional Optical Lattices Approaching the Tonks-Girardeau Regime

“…Recent studies of the one-dimensional Bose-Hubbard model mainly focused on the Mott-superfluid transition, using a wide range of methods: a slave-boson approach [12], the numerical renormalization group [13], the density matrix renormalization group [14], the time-evolving block decimation method [15] and Monte Carlo methods [16].…”

“…2 that a Mott-like region is formed in the center of the trap. For a homogeneous system in the Mott phase, the dispersion relation of the excitations has a gap of order U [11], meaning that the role of double occupancies is strongly suppressed [13]. The Mott phase is entered at a ratio U/J as low as 1.67 at T = 0 for a density of one particle per site [25].…”