Efficient iterative diagonalization of the Bose-Hubbard model for ultracold bosons in a periodic optical trap

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Composite electronic systems are sometimes modeled by the Bose-Hubbard Hamiltonian. Iterative solution of this model, yielding a handful of the lowest-lying states is presented. The effect of the Hamiltonian on the trial vector is evaluated in a direct manner. A representation on the basis of sites is adopted, the rate limiting factor being merely the one-body term in such circumstances. The iteration follows the scheme of Davidson and provides exact states and state energies of the model Hamiltonian. Exponential dependence of the memory requirement on the number of bosons and lattice sites sets the limit of applicability to small systems. Restriction of the maximal occupation of sites is investigated in order to reduce the actual memory need. The energy error introduced this way ranges from negligible (in the strong-coupling limit) to substantial (in the weak-coupling limit).

Original languageEnglish
Pages (from-to)208-216
Number of pages9
JournalChemical Physics
Publication statusPublished - Jun 5 2012



  • Bose-Hubbard model
  • Direct CI
  • Iterative diagonalization

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

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