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

Autor:	Boland, G.
Rok vydání:	2010
Předmět:	Condensed Matter - Statistical Mechanics Condensed Matter - Quantum Gases
Druh dokumentu:	Working Paper
Popis:	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. Comment: Version published in JMP
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1002.3079 Zobrazit plný text záznamu View this record from Arxiv