arXiv:0810.0643 · Physical Review B

Bose-Hubbard phase diagram with arbitrary integer filling

Niklas Teichmann, Dennis Hinrichs, Martin Holthaus, André Eckardt

Published Mar 6, 2009• 65 citations

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.

DOI: 10.1103/physrevb.79.100503

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arXiv:0810.0643 · Physical Review B

Bose-Hubbard phase diagram with arbitrary integer filling

Niklas Teichmann, Dennis Hinrichs, Martin Holthaus, André Eckardt

Published Mar 6, 2009• 65 citations

arXiv HTML PDF

Abstract

d>3

and to the quantum rotor limit of high filling, which refers to an array of Josephson junctions.

DOI: 10.1103/physrevb.79.100503

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arXiv:cond-mat/0701178Physical Review BApr 16, 2007296 citations

d>3

and to the quantum rotor limit of high filling, which refers to an array of Josephson junctions.

d>3

, thus monitoring the approach to the mean-field limit. The versatility of the method suggests further applications to other systems which are less well understood.

We study the quantum phase transition between the insulating and the globally coherent superfluid phases in the Bose-Hubbard model with

{\mathcal{T}}_{3}

structure, the ``dice lattice.'' Even in the absence of any frustration the superfluid phase is characterized by modulation of the order parameter on the different sublattices of the

{\mathcal{T}}_{3}

structure. The zero-temperature critical point as a function of magnetic field shows the characteristic ``butterfly'' form. At full frustration the superfluid region is strongly suppressed. In addition, due to the existence of the Aharonov-Bohm cages at

f=1∕2

, we find some evidence for the existence of an intermediate insulating phase characterized by a zero superfluid stiffness but finite compressibility. In this intermediate phase bosons are localized due to the external frustration and the topology of the

{\mathcal{T}}_{3}

lattice. We name this new phase the Aharonov-Bohm insulator. In the presence of charge frustration the phase diagram acquires the typical lobe structure. The form and hierarchy of the Mott insulating states with fractional fillings are dictated by the particular topology of the

{\mathcal{T}}_{3}

lattice. The results presented were obtained by a variety of analytical methods: mean-field and variational techniques to approach the phase boundary from the superconducting side and a strongly coupled expansion appropriate for the Mott insulating region. In addition we performed quantum Monte Carlo simulations of the corresponding

(2+1)

-dimensional

XY

model to corroborate the analytical calculations with a more accurate quantitative analysis. We finally discuss experimental realization of the

{\mathcal{T}}_{3}

lattice both with optical lattices and with Josephson junction arrays.

n=1

is found to be at

{(U∕t)}_{\mathrm{c}}=29.34(2)

, and the insulating gap $\ensuremath{\Delta}$ is measured with accuracy of a few percent of the hopping amplitude

t

. We obtain the effective mass of particle and hole excitations in the insulating state---with explicit demonstration of the emerging particle-hole symmetry and relativistic dispersion law at the transition tip---along with the sound velocity in the strongly correlated superfluid phase. These parameters are the necessary ingredients to perform analytic estimates of the low temperature $(T⪡\ensuremath{\Delta})$ thermodynamics in macroscopic samples. We present accurate thermodynamic curves, including these for specific heat and entropy, for typical insulating

(U∕t=40)

and superfluid

(t∕U=0.0385)

phases. Our data can serve as a basis for accurate experimental thermometry, and a guide for appropriate initial conditions if one attempts to use interacting bosons in quantum information processing.