Séminaire GPP

Wednesday 12 Oct 2016, 15:00 → 17:00 Europe/Brussels

E349 (Marc de Hemptinne)

Pieter W. Claeys : Richardson-Gaudin models: What can we learn from (breaking) symmetry ? Richardson-Gaudin integrable models hold a special place within the general framework of manybody systems. While their underlying algebraic structure allows for an exact solution by Bethe Ansatz, the large freedom left in their construction allows them to be linked to an extensive range of physical phenomena such as superconductivity and quantum magnetism. In this talk, I will focus on the class of hyperbolic Richardson-Gaudin models. After a general introduction to these models, their remarkable symmetries will be introduced and discussed. It will be shown how these symmetries can be exploited in order write down expressions for physical observables as determinants of matrices. Furthermore, by breaking the u(1) symmetry of these models, the subtle interplay between different symmetry sectors can be uncovered, shedding some light on the structure of the (Bethe Ansatz) wave functions. Throughout this talk, the general theory will be applied to a specific model which describes topological superconductivity, highlighting the physical consequences of these results. The talk will mainly be based on these two recent papers : [1] P. W. Claeys, S. De Baerdemacker, M. Van Raemdonck, and D. Van Neck, Phys. Rev. B 91, 155102 (2015). [2] P. W. Claeys, S. De Baerdemacker, and D. Van Neck, Phys. Rev. B 93, 220503(R) (2016).