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Acta Physica Polonica A

Phase Transitions in Optical Lattices at Finite Temperatures

T. P. Polak, T. K. Kopeć

Published Jan 1, 2009• 0 citations
Publisher

Abstract

We discuss the finite-temperature phase diagram in three-dimensional Bose-Hubbard model relevant for the Bose-Einstein condensates in optical lattices, by employing U(1) quantum rotor approach and the topologically constrained path integral, that includes a summation over U(1) topological charge.The effective action formalism allows us to formulate a problem in the phase only action and obtain analytical formulae for the critical lines beyond mean-field theory.

DOI
10.12693/aphyspola.115.418

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We present an approach to the Bose-Hubbard model using the U(1) quantum rotor description. The effective action formalism allows us to formulate a problem in the phase only action and obtain analytical formulas for the critical lines. We show that the nontrivial U(1) phase field configurations have an impact on the phase diagrams. The topological character of the quantum field is governed by terms of the integer charges---winding numbers. The comparison of presented results to recently obtained quantum Monte Carlo numerical calculations suggests that the competition between quantum effects in strongly interacting boson systems is correctly captured by our model.
We present the novel approach to the Bose-Hubbard model using the U(1) quantum rotor description.We formulate a problem in the phase only action using an effective action formalism and obtain analytical formulae for the critical lines.We show that the nontrivial U(1) phase field configurations have an impact on the phase diagrams.The topological character of the quantum field is governed by terms of the integer charges -winding numbers n.The comparison of the presented results with recently obtained quantum Monte Carlo numerical calculations suggests that the competition between quantum effects in strongly interacting boson systems is correctly captured by our model.
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Abstract The physics of the Bose–Hubbard (BH) model is the subject of intensive studies in recent years, since it has been realized that BH Hamiltonian can be applied to systems of cold atoms confined in periodic optical lattice potential, where the effects on interactions are strongly enhanced. Our aim is to extend the widely used mean‐field treatment of the superfluid–Mott insulator (SF–MI) transition in the BH model. Our method also improves the strong‐coupling expansion that works well only for sufficiently large insulating gap. The key point of the approach is to consider the representation of strongly interacting bosons as particles with attached U(1) gauge group flux tubes, which constitutes the quantum rotor description. The effective action formalism allows us to cast the problem in terms of the phaseonly action and obtain an analytical formulas for critical lines. Finally, we calculate the zero‐temperature SF–MI phase diagrams for three‐dimensional BH model and compare our results with the outcome of numerical Monte Carlo simulations. We found a very good agreement for the quantitative results regarding the details of the lobe in the phase diagrams showing the quantum transition from superfluid to the Mott insulating phase (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
We discuss the ground state of the two-dimensional Bose-Hubbard (BH) Hamiltonian, relevant for rotating gaseous Bose-Einstein condensates, by employing U(1) quantum rotor approach and the topologically constrained path integral that includes a summation over U(1) topological charge. We derive an effective quantum action for the BH model, which enables a nonperturbative treatment of the zero-temperature phase transition. We calculate the ground-state phase diagram, analytically deriving maximum repulsive energy for several rational values of the frustration rotation parameter f=0f=0f=0, 1/2, 1/3, 1/4, and 1/6 for the square and triangular lattices, which improves upon previous theoretical treatments. The ground state of the rotating Bose-Einstein condensates on a triangular lattice appears to be most stable against the effects of rotation. Performed calculations revealed strong dependence of the critical ratio of the kinetic energy to the repulsive on-site energy, which separates the global coherent from the insulating state, on topology of the lattice.