Long Cycles in the Infinite-Range-Hopping Bose-Hubbard Model

G. Boland

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arXiv · 1002.3079

Long Cycles in the Infinite-Range-Hopping Bose-Hubbard Model

G. Boland

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Abstract

In this paper we study the relation between long cycles and Bose-Einstein condensation in the Infinite-Range Bose-Hubbard Model. We obtain an expression for the cycle density involving the partition function for a Bose-Hubbard Hamiltonian with a single-site correction. Inspired by the Approximating Hamiltonian method we conjecture a simplified expression for the short cycle density as a ratio of single-site partition functions. In the absence of condensation we prove that this simplification is exact and use it to show that in this case the long-cycle density vanishes. In the presence of condensation we can justify this simplification when a gauge-symmetry breaking term is introduced in the Hamiltonian. Assuming our conjecture is correct, we compare numerically the long-cycle density with the condensate and find that though they coexist, in general they are not equal.

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G. Boland. 2010-02-16. Long Cycles in the Infinite-Range-Hopping Bose-Hubbard Model. https://arxiv.org/abs/1002.3079

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