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

A. Szabados, Péter Jeszenszki, P. Surján

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

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
Volume401
DOIs
Publication statusPublished - Jun 5 2012

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Hamiltonians
Hubbard model
Bosons
bosons
traps
Data storage equipment
iterative solution
occupation
Electron energy levels
iteration
constrictions
requirements
composite materials
energy
Composite materials
electronics

Keywords

  • Bose-Hubbard model
  • Direct CI
  • Iterative diagonalization

ASJC Scopus subject areas

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

Cite this

Efficient iterative diagonalization of the Bose-Hubbard model for ultracold bosons in a periodic optical trap. / Szabados, A.; Jeszenszki, Péter; Surján, P.

In: Chemical Physics, Vol. 401, 05.06.2012, p. 208-216.

Research output: Contribution to journalArticle

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