Hubbard Model in Dynamical Mean-Field Theory

Vladimir Anisimov, Yuri Izyumov

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


Let us consider standard Hubbard model for nondegenerate electrons. 3.1.1$$ \hat H = \sum\limits_{ij\sigma } {t_{ij} \hat c_{i\sigma }^ + \hat c_{j\sigma } + \sum\limits_i {U \hat n_{i\uparrow} \hat n_{i\downarrow},} } $$ where$$ \hat c_{i\sigma }^ + (\hat c_{i\sigma } ) $$ are creation (annihilation) operators for electron on site i with spin$$ \sigma = \uparrow, \downarrow ;\hat n_{i\sigma } = \hat c_{i\sigma }^ + \hat c_{i\sigma } $$ the number of electrons operator in state iσ, tij is the matrix element for electron hopping from site j to site i, U is Coulomb interaction energy for two electrons on the same site.

Original languageEnglish
Title of host publicationSpringer Series in Solid-State Sciences
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages74
Publication statusPublished - 2010
Externally publishedYes

Publication series

NameSpringer Series in Solid-State Sciences
ISSN (Print)0171-1873
ISSN (Electronic)2197-4179


  • Green Function
  • Hubbard Band
  • Hubbard Model
  • Quantum Monte Carlo
  • Retarded Green Function


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