Bose-Hubbard phase diagram with arbitrary integer filling

Abstract

We study the transition from a Mott insulator to a superfluid in both the two- and the three-dimensional Bose-Hubbard model at zero temperature, employing the method of the effective potential. Converting Kato's perturbation series into an algorithm capable of reaching high orders, we obtain accurate critical parameters for any integer filling factor. Our technique allows us to monitor both the approach to the mean-field limit by considering spatial dimensionalities $d > 3$, and to the quantum rotor limit of high filling, which refers to an array of Josephson junctions.Comment: 4 pages, 4 figure

Tuning the quantum phase transition of bosons in optical lattices via periodic modulation of thes-wave scattering length

“…2 that the QMC result lies between the third-order strong-coupling result and the second-order EPLT result. This suggests to evaluate both analytical methods to even higher hopping orders, for instance, by applying the process-chain approach [43]. The true quantum phase boundary should then lie between the upper boundary provided by the strong-coupling method and the lower boundary from the EPLT method.…”

“…Whereas the lowest order of EPLT leads to similar results as mean-field theory [1], higher hopping orders have recently been evaluated via the process-chain approach [43], which determines the location of the quantum phase transition to a similar precision as demanding quantum Monte Carlo simulations [44]. Here we follow Refs.…”

Mott glass to superfluid transition for random bosons in two dimensions

“…For the closest approach to criticality with the initial distributions described in Appendix C, we find that the ratio Jtyp Ω is approximately 0.11 ± 0.01 near the fixed point. Hence, the typical link is quantitatively weak compared to J U ≈ 0.345 at the clean transition 22 . The considerations above form a strong argument for the validity of the site decimation RG step.…”

“…When the Josephson couplings J jk and charging energies U j are uniform, the rotor model (7) exhibits a quantum phase transition between superfluid and Mott insulating phases at zero temperature. This transition is in the universality class of the three-dimensional classical XY model 3,4,21 , and one recent study determines that the transition occurs at J U ≈ 0.345 22 . The critical exponent governing the divergence of the correlation length at the clean transition is ν ≈ 0.663 23 .…”

Even-odd correlation functions on an optical lattice

“…Following Freericks et al [15], and the related works of Eckardt et al [16,17], we perturbatively calculate the nearest-neighbor correlator in powers of t/U . This expansion breaks down in the superfluid phase, but captures the leading order correlations in the Mott phases.…”