2006/11/30 by N. Oelkers, Norman Oelkers, Jon Links · 82 citations
Physics and Astronomy · #Bethe ansatz #Cold Atom Physics and Bose-Einstein Condensates #Computer science #Crossover #Excited state #Ground state #Hubbard model #Lattice (music) #Limiting #Mean field theory #Physics #Physics of Superconductivity and Magnetism #Quantum mechanics #Statistical physics #Strong Light-Matter Interactions #Superconductivity #Wave function #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevb.75.115119
published in Physical Review B 75(11) (American Physical Society) · 17 pages, 12 figures, Phys.Rev.B(accepted), minor changes and updated references
arxiv created 2007/03/06 · openalex publication_date 2007/03/19 · arxiv updated 2013/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.