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Theoretical and Mathematical Physics

Bound states and poles of the two-particle Green's function

A. Karimkhodzhaev, Rudolf Nikolaevich Faustov

Published Jan 1, 1977• 8 citations
Publisher
DOI
10.1007/bf01029353

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The equation in the ladder approximation was derived for the two-particle Green function of the itinerant electrons with the Heisenberg ferromagnetic and antiferromagnetic interaction. The general form of its solution was found. The existence of the pole in this solution is related to the condensation of the bound pairs in the corresponding spin state. The condition for the pole determines the critical temperature T c . The effective interaction between the mobile holes due to the mobile hole-localized spin coupling in the two-band Hubbard model was also studied.
The normal state temperature one- and two-particle Green’s functions are calculated within the framework of the conserving self-consistent approximation accounting for the fluctuations in the particle-particle channel for the attractive Hubbard model. The Pad´e continuation to the complex plane is used to study the pole structure of the retarded one-particle Green’s function. The momentum and temperature dependences of the positions of the leading quasiparticle poles are consistent with Bogolyubov’s picture, when the second leading pole emerges and rapidly moves toward the real axes. The non-Fermi liquid behavior of the first leading pole is detected at the intermediate coupling. The two-particle Green’s function is used to calculate the temperature dependence of the uniform static spin susceptibility, which is shown to exhibit the diamagnetic tendency, as the system approaches the superconducting phase transition.
The problem of a Dirac particle moving in a deformed Hulthén potential is solved in the framework of the path integral formalism. With the help of the Biedenharn transformation, the construction of a closed form for the Green’s function of the second-order Dirac equation is done by using a proper approximation to the centrifugal term and the Green’s function of the linear Dirac equation is calculated. The energy spectrum for the bound states is obtained from the poles of the Green’s function. A Dirac particle in the standard Hulthén potential ( q = 1) and a Dirac hydrogen-like ion ( q = 1 and a → ∞) are considered as particular cases.