TBA and tree expansion

Ivan Kostov (1) , Didina Serban (1) , Dinh-Long Vu (1)

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681

We propose an alternative, statistical, derivation of the Thermodynamic Bethe Ansatz based on the tree expansion of the Gaudin determinant. We illustrate the method on the simplest example of a theory with diagonal scattering and no bound states. We reproduce the expression for the free energy density and the finite size corrections to the energy of an excited state as well as the LeClair-Mussardo series for the one-point function for local operators.

Mots clés: Bethe ansatz: thermodynamical; correction: finite size; excited state: energy; free energy: density; operator: local; determinant; bound state; statistical; scattering; Thermodynamic Bethe Ansatz; Integrable models; Matrix-Tree Theorem

Domaines: Physique des Hautes Energies - Théorie [hep-th]

Ivan Kostov, Didina Serban, Dinh-Long Vu. TBA and tree expansion. 10th International Symposium on Quantum theory and symmetries and 12th International Workshop on Lie Theory and Its Applications in Physics, Jun 2017, Varna, Bulgaria. pp.77-98, ⟨10.1007/978-981-13-2179-5_6⟩. ⟨hal-01797135⟩