The exactly solvable BCS Hamiltonian of superconductivity is considered from several viewpoints: Richardson's ansatz, conformal field theory, integrable inhomogenous vertex models and Chern-Simons theory.

arXiv:hep-th/0111114Nov 13, 20013 citations

arXiv:hep-th/9911078 · Nuclear Physics B

Conformal field theory and the exact solution of the BCS Hamiltonian

Germán Sierra

Published Apr 1, 2000• 55 citations

arXiv HTML PDF

DOI: 10.1016/s0550-3213(00)00036-5

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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.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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Integrability and Conformal Symmetry in the BCS model

G. Sierra

arXiv:hep-th/0111114Nov 13, 20013 citations

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.