Conformal Field Theory and the Exact Solution of the BCS Hamiltonian

Details Conformal Field Theory and the Exact Solution of the BCS Hamiltonian Conformal Field Theory and the Exact Solution of the BCS Hamiltonian

1999-11-11

arxiv.org/abs/hep-th/9911078v1

Nucl.Phys. B572 (2000) 517-534

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, RevTex

Scientific paper

10.1016/S0550-3213(00)00036-5

We propose a connection between conformal field theory (CFT) and the exact solution and integrability of the reduced BCS model of superconductivity. The relevant CFT is given by the $SU(2)_k$-WZW model in the singular limit when the level k goes to -2. This theory has to be perturbed by an operator proportional to the inverse of the BCS coupling constant. Using the free field realization of this perturbed Wess-Zumino-Witten model, we derive the exact Richardson's wave function and the integrals of motion of the reduced BCS model in the saddle point approximation. The construction is reminiscent of the CFT approach to the Fractional Quantum Hall effect.

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