Archive ouverte HAL – The equilibrium landscape of the Heisenberg spin chain

Enej IlievskiEoin Quinn 1

Enej Ilievski, Eoin Quinn. The equilibrium landscape of the Heisenberg spin chain. SciPost Physics, SciPost Foundation, 2019, 7 (3), ⟨10.21468/SciPostPhys.7.3.033⟩. ⟨hal-02295879⟩

We characterise the equilibrium landscape, the entire manifold of local equilibrium states, of an interacting integrable quantum model. Focusing on the isotropic Heisenberg spin chain, we describe in full generality two complementary frameworks for addressing equilibrium ensembles: the functional integral Thermodynamic Bethe Ansatz approach, and the lattice regularisation transfer matrix approach. We demonstrate the equivalence between the two, and in doing so clarify several subtle features of generic equilibrium states. In particular we explain the breakdown of the canonical Y-system, which reflects a hidden structure in the parametrisation of equilibrium ensembles.

  • 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques