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arXiv:0704.3774 · Physical Review B

Mott insulator–superfluid transitions in a two-band model at finite temperature and possible application to supersolid He4

Huai-Bin Zhuang, Michael Ma, Xi Dai, Fu‐Chun Zhang

Published Nov 7, 2007• 4 citations
arXivHTMLPDF

Abstract

We study the Mott insulator--superfluid transition in a two-band boson Hubbard model, which can be mapped onto a spin-$1∕2$ $XY$ model with spins coupled to an additional Ising degree of freedom. By using a modified mean field theory that includes the effects of phase fluctuations, we show that the transition is first order at both zero and finite temperatures. On the Mott insulator side, there may be reentrance in phase transition. These features are consequences of the underlying transition between competing defect poor and defect rich phases. The possible relevance of the model and our results to supersolid $^{4}\mathrm{He}$ and cold bosonic atoms in optical lattices are discussed.

DOI
10.1103/physrevb.76.174504

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We describe the ground state of a gas of bosonic atoms with two coherently coupled internal levels in a deep optical lattice in a one-dimensional geometry. In the single-band approximation this system is described by a Bose-Hubbard Hamiltonian. The system has a superfluid and a Mott insulating phase that can be either paramagnetic or ferromagnetic. We characterize the quantum phase transitions at unit filling by means of a density-matrix renormalization-group technique and compare the results with a mean-field approach and an effective spin Hamiltonian. The presence of the ferromagnetic Ising-like transition modifies the Mott lobes. In the Mott insulating region the system maps to the ferromagnetic spin-1/2 XXZXXZXXZ model in a transverse field and the numerical results compare very well with the analytical results obtained from the spin model. In the superfluid regime quantum fluctuations strongly modify the phase transition with respect to the well-established mean-field three-dimensional classical bifurcation.
The Bose Hubbard model describing interacting bosons in an optical lattice is reduced to a simple spin-1 XY model with single-ion anisotropy in the vicinity of the Mott phase. In the strong coupling Mott insulating regime, we propose a mean field theory based on a constraint SU (3) pseudo-boson representation on the effective model and discuss the excitation spectra and the phase transition to the superfluid state. Further to the superfluid phase, we use the coherent-state approach to derive the collective excitation modes. It is found that the Mott phase has two degenerate gapped quadratic excitation spectra which graduate into two degenerate gapless linear ones at the transition point, and one gapless linear mode with one gapped quadratic mode in the superfluid phase.