Two-particle states in the Hubbard model

2008/05/31 by Manuel Valiente, David Petrosyan · 1 citation
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Quantum many-body systems #Strong Light-Matter Interactions #math-ph #math.MP #quant-ph

paper · pdf · doi:10.1088/0953-4075/41/16/161002

published as J. Phys. B: At. Mol. Opt. Phys. 41, 161002 (2008) · 3 pages, 1 figure

arxiv created 2008/06/18 · openalex publication_date 2008/08/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

We consider a pair of bosonic particles in a one-dimensional tight-binding periodic potential described by the Hubbard model with an attractive or repulsive on-site interaction. We derive explicit analytic expressions for the two-particle states, which can be classified as (i) scattering states of asymptotically free particles and (ii) interaction-bound dimer states. Our results provide a very transparent framework to understand the properties of interacting pairs of particles in a lattice.

Citations

• Tunneling couplings in discrete lattices, single-particle band structure, and eigenstates of interacting atom pairs
• Dynamics of Bose-Einstein condensates in optical lattices
• Repulsively bound atom pairs in an optical lattice

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