Integrability of the russian doll BCS model

Details Integrability of the russian doll BCS model Integrability of the russian doll BCS model

2004-06-10

arxiv.org/abs/cond-mat/0406234v1

Nucl.Phys. B702 (2004) 481-494

Physics

Condensed Matter

Statistical Mechanics

14 pages, 7 figures, latex

Scientific paper

10.1016/j.nuclphysb.2004.09.021

We show that integrability of the BCS model extends beyond Richardson's model (where all Cooper pair scatterings have equal coupling) to that of the russian doll BCS model for which the couplings have a particular phase dependence that breaks time-reversal symmetry. This model is shown to be integrable using the quantum inverse scattering method, and the exact solution is obtained by means of the algebraic Bethe ansatz. The inverse problem of expressing local operators in terms of the global operators of the monodromy matrix is solved. This result is used to find a determinant formulation of a correlation function for fluctuations in the Cooper pair occupation numbers. These results are used to undertake exact numerical analysis for small systems at half-filling.

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