Functional-derivative study of the Hubbard model. III. Fully renormalized Green's function

Journal Article · Tue Apr 15 04:00:00 EST 1980 · Phys. Rev., B: Condens. Matter; (United States)

DOI:https://doi.org/10.1103/PhysRevB.21.3300· OSTI ID:5315240

Arai, T; Cohen, M H

The functional-derivative method of calculating the Green's function developed earlier for the Hubbard model is generalized and used to obtain a fully renormalized solution. Higher-order functional derivatives operating on the basic Green's functions, G and GAMMA, are all evaluated explicitly, thus making the solution applicable to the narrow-band region as well as the wide-band region. Correction terms Phi generated from functional derivatives of equal-time Green's functions of the type delta/sup n/ < N > /deltaepsilon/sup n/, etc., with n > or = 2. It is found that the Phi's are, in fact, renormalization factors involved in the self-energy ..sigma.. and that the structure of the Phi's resembles that of ..sigma.. and contains the same renormalization factors Phi. The renormalization factors Phi are shown to satisfy a set of equations and can be evaluated self-consistently. In the presence of the Phi's, all difficulties found in the previous results (papers I and II) are removed, and the energy spectrum ..omega.. can now be evaluated for all occupations n. The Schwinger relation is the only basic relation used in generating this fully self-consistent Green's function, and the Baym-Kadanoff continuity condition is automatically satisfied.

• Research Organization: Argonne National Laboratory, Argonne, Illinois 60439
• OSTI ID: 5315240
• Journal Information: Phys. Rev., B: Condens. Matter; (United States), Journal Name: Phys. Rev., B: Condens. Matter; (United States) Vol. 21:8; ISSN PRBMD
• Country of Publication: United States
• Language: English

Related Subjects

656000* -- Condensed Matter Physics
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
BAND THEORY
CRYSTALS
ENERGY
FUNCTIONS
GREEN FUNCTION
RENORMALIZATION
SELF-ENERGY