A distribution approach to finite-size corrections in Bethe Ansatz solvable models

Etienne Granet (1, 2) , Jesper Lykke Jacobsen (1, 2) , Hubert Saleur (1, 3)

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681
2 LPTENS - Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure]
3 UCLA - University of California [Los Angeles]

We present a new and efficient method for deriving finite-size effects in statistical physics models solvable by Bethe Ansatz. It is based on the study of the functional that maps a function to the sum of its evaluations over the Bethe roots. A simple and powerful constraint is derived when applying this functional to infinitely derivable test functions with compact support, that generalizes then to more general test functions.The method is presented in the context of the simple spin-1/2 XXZ chain for which we derive the finite-size corrections to leading eigenvalues of the Hamiltonian for any configuration of Bethe numbers with real Bethe roots. The expected results for the central charge and conformal dimensions are recovered.

Domaines: Physique mathématique [math-ph]

Etienne Granet, Jesper Lykke Jacobsen, Hubert Saleur. A distribution approach to finite-size corrections in Bethe Ansatz solvable models. Nuclear Physics B, 2018, 934, pp.96-117. ⟨10.1016/j.nuclphysb.2018.06.001⟩. ⟨hal-01851164⟩