Functional-derivative study of the Hubbard model. II. Self-consistent equation and its complete solution

Journal Article · Tue Feb 15 04:00:00 EST 1977 · Phys. Rev., B; (United States)

DOI:https://doi.org/10.1103/PhysRevB.15.1836· OSTI ID:7325287

Arai, T; Cohen, M H

We develop a self-consistent method to solve the basic equation for the self-energy correction of the Hubbard model obtained previously. The term ..pi..(..delta..) involving second functional derivatives is neglected, and the quantities < N/sub R sigma/(t) > and < C/sub R sigma//sup dagger/(t) C/sub R'' sigma/(t) > are initially assumed to be independent of the external fields epsilon(sigma) and epsilon(sigma-bar). Under these restrictions, the complete self-energy correction is shown to be expanded in powers of epsilon (sigma) and epsilon (sigma-bar) in the form ..sigma../sub R R prime sigma/(tt') = xi/sub 0/(RR'sigma-bart) delta/sub tt'/ + ..sigma../sub n//sub 0/ ..sigma../sub R prime prime/ ..sigma../sub R prime prime prime/ xi/sup( n)/ (RR';R''R''') epsilon (R''R'''sigmat) delta/sub t t prime/, where xi/sub 0/ consists of all possible terms linear in epsilon (sigma-bar), while xi/sup( n)/ is made up of all possible terms of the nth degree in epsilon (sigma-bar). Equations for xi/sub 0/ and xi/sup( n)/ are solved exactly and the resulting series is summed analytically, yielding a compact and complete analytic solution for the restricted equation results. The part which is linear in epsilon is shown to be equal to the perturbation result obtained in the previous paper;the claim that the perturbation result is exact through terms linear in epsilon is thus confirmed. The method is extended and the effect of delta < N >/deltaepsilon and delta< C/sup dagger/C > /deltaepsilon is included. The effect is found to eliminate the difficulty that the value of one of the terms in the self-energy correction is abnormally overestimated in the previous result in the split-band, half-filled limit.

• Research Organization: Argonne National Laboratory, Argonne, Illinois 60439
• OSTI ID: 7325287
• Journal Information: Phys. Rev., B; (United States), Journal Name: Phys. Rev., B; (United States) Vol. 15:4; ISSN PLRBA
• Country of Publication: United States
• Language: English

Related Subjects

656000* -- Condensed Matter Physics
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
CORRECTIONS
ELECTRONIC STRUCTURE
ELEMENTS
ENERGY
FUNCTIONALS
FUNCTIONS
GREEN FUNCTION
METALS
SELF-CONSISTENT FIELD
SELF-ENERGY
TRANSITION ELEMENTS