ZhETF, Vol. 138,
p. 107 (July 2010)
(English translation - JETP,
Vol. 111, No. 1,
available online at www.springer.com
DIAGRAM ANALYSIS OF THE HUBBARD MODEL: STATIONARITY PROPERTY OF THE THERMODYNAMIC POTENTIAL
Moskalenko V.A., Dohotaru L.A., Cebotari I.D.
Received: October 5, 2009
The diagram approach proposed many years ago for the strongly correlated Hubbard model is developed with the aim to analyze the thermodynamic potential properties. A new exact relation between renormalized quantities such as the thermodynamic potential, the one-particle propagator, and the correlation function is established. This relation contains an additional integration of the one-particle propagator with respect to an auxiliary constant. The vacuum skeleton diagrams constructed from the irreducible Green's functions and tunneling propagator lines are determined and a special functional is introduced. The properties of this functional are investigated and its relation to the thermodynamic potential is established. The stationarity property of this functional with respect to first-order variations of the correlation function is demonstrated; as a consequence, the stationarity property of the thermodynamic potential is proved.