The electron gas with a strong pairing interaction: Three particle correlations and the Thouless instability

Details The electron gas with a strong pairing interaction: Three particle correlations and the Thouless instability The electron gas with a strong pairing interaction: Three particle correlations and the Thouless instability

2000-09-18

arxiv.org/abs/cond-mat/0009262v1

Phys.Rev.B64:144519,2001

Physics

Condensed Matter

Strongly Correlated Electrons

14 pages, 9 figures

Scientific paper

10.1103/PhysRevB.64.144519

We derive simplified Faddeev type equations for the three particle T-matrix which are valid in the Hubbard model where only electrons with opposite spins interact. Using the approximation of dynamical mean field theory these equations are partially solved numerically for the attractive Hubbard model. It is shown that the three particle T-matrix contains a term vanishing $\sim T^2$ at the Thouless (or BCS) instability where the two-particle T-matrix diverges. Based on the three particle term we further derive the low density - strong coupling extension for the two-particle vertex function. We therefore understand our equations as a step towards a systematic low density expansion from the weak coupling BCS theory towards the stronger coupling limit.

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