QUANTUM
   INTEGRABLE
   SYSTEMS and
   GEOMETRY
   2012









 3-7 SEPTEMBER 2012
 OLHÃO, PORTUGAL

The Tamm-Dancoff Approximation as the Richardson-Gaudin equations in the contraction limit

Stijn De Baerdemacker

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The Bardeen-Cooper-Schrieffer (BCS) Hamiltonian is an essential ingredient for the description of pairing phenomena in many-body systems, such as e.g. condensed matter or atomic nuclei. Richardson and Gaudin have demonstrated that the level-independent BCS Hamiltonian is integrable and exactly solvable with a Bethe Ansatz, provided the variables in the Ansatz satisfy the set of coupled non-linear Richardson-Gaudin (RG) equations. In this contribution, it will be discussed how the RG equations are related to the secular equation of the Tamm-Dancoff Approximation of the BCS Hamiltonian. By means of a deformation of the su(2) quasi-spin algebra, it can be shown that the non-linear coupling in the RG equations is a direct consequence of the Pauli exclusion effect in the fermionic realisation of the quasi-spin algebra.