Particlehole duality, integrability, and Russian doll BCS model
Abstract
We address a generalized Richardson model (Russian doll BCS model), which is characterized by the breaking of timereversal symmetry. This model is known to be exactly solvable and integrable. We point out that the Russian doll BCS model, on the level of Hamiltonian, is also particlehole symmetric. This implies that the same state can be expressed both in the particle and hole representations with two different sets of Bethe roots. We then derive exact relations between Bethe roots in the two representations, which can hardly be obtained staying on the level of Bethe equations. In a quasiclassical limit, similar identities for usual Richardson model, known from literature, are recovered from our results. We also show that these relations for Richardson roots take a remarkably simple form at halffilling and for a symmetric with respect to the middle of the interaction band distribution of onebody energy levels, since, in this special case, the rapidities in the particle and hole representations up to the translation satisfy the same system of equations.
 Publication:

Nuclear Physics B
 Pub Date:
 August 2015
 DOI:
 10.1016/j.nuclphysb.2015.05.031
 arXiv:
 arXiv:1412.1016
 Bibcode:
 2015NuPhB.897..405B
 Keywords:

 Condensed Matter  Superconductivity;
 Condensed Matter  Mesoscale and Nanoscale Physics;
 High Energy Physics  Theory;
 Mathematical Physics;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 15 pages, 2 figures