Ground-state properties of the attractive one-dimensional Bose-Hubbard model

Oelkers, N. and Links, J. (2007) Ground-state properties of the attractive one-dimensional Bose-Hubbard model. Physical Review B, 75 11: 115119-1-115119-15. doi:10.1103/PhysRevB.75.115119

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Author Oelkers, N.
Links, J.
Title Ground-state properties of the attractive one-dimensional Bose-Hubbard model
Journal name Physical Review B   Check publisher's open access policy
ISSN 1098-0121
Publication date 2007
Sub-type Article (original research)
DOI 10.1103/PhysRevB.75.115119
Open Access Status File (Publisher version)
Volume 75
Issue 11
Start page 115119-1
End page 115119-15
Total pages 15
Editor Adams, P. D.
Place of publication United States
Publisher American Physical Society
Collection year 2008
Language eng
Subject 230199 Mathematics not elsewhere classified
240201 Theoretical Physics
780101 Mathematical sciences
0105 Mathematical Physics
Abstract We study the ground state of the attractive one-dimensional Bose-Hubbard model, and in particular the nature of the crossover between the weak interaction and strong interaction regimes for finite system sizes. Indicator properties such as the gap between the ground and first excited energy levels, and the incremental ground-state wave function overlaps are used to locate different regimes. Using mean-field theory we predict that there are two distinct crossovers connected to spontaneous symmetry breaking of the ground state. The first crossover arises in an analysis valid for large L with finite N, where L is the number of lattice sites and N is the total particle number. An alternative approach valid for large N with finite L yields a second crossover. For small system sizes we numerically investigate the model and observe that there are signatures of both crossovers. We compare with exact results from Bethe ansatz methods in several limiting cases to explore the validity for these numerical and mean-field schemes. The results indicate that for finite attractive systems there are generically three ground-state phases of the model.
Keyword Physics, Condensed Matter
Q-Index Code C1
Q-Index Status Confirmed Code

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Created: Thu, 24 Apr 2008, 12:49:09 EST by Marie Grove on behalf of School of Mathematics & Physics