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On Functional Fourier Transformation for the Hubbard Model and Similar Models
Author(s) -
Behn U.,
Weller W.
Publication year - 1980
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2220990105
Subject(s) - hubbard model , electron , transformation (genetics) , fermion , physics , function (biology) , mathematical physics , fourier transform , statistical physics , quantum mechanics , mathematics , superconductivity , chemistry , biochemistry , evolutionary biology , biology , gene
Describing spin ↑ ‐electrons the particle number operators n i ↓ are replaced under the functional integral directly by c ‐numbers v i ↓( t ) using a δ‐functional instead of the Hubbard‐Stratonovich transformation. The Green function of the Hubbard model is thus exactly represented as an averaged Green function of electrons moving in a stochastic potential Uv i ↓( t ). The probability distribution for the stochastic process v ↓ containing the many body aspect and the information about the ↓‐electrons is determined. The v i ↓( t ) are only allowed to jump between 0 and 1 reflecting the property of Fermion particle number operators. This exact scheme can be interpreted as a dynamically generalized alloy analogy.