We will discuss the effective Hamiltonian that generates time evolution of states on intermediate time scales in the strong-coupling limit of the spin-1/2 XXZ model. To leading order, such an effective Hamiltonian describes an integrable model with local interactions. I will present a full coordinate Bethe Ansatz solution that manifestly breaks the translational symmetry of the model, and describe its quasi-particle content. The corresponding Bethe equations are completely solvable, allowing for exact characterisation of degeneracies, as well as specification of a generic (thermodynamically relevant) state. I will also discuss jammed states and their stability under the leading correction to the effective Hamiltonian. Finally, if time permits, I will also visit the subjects of Thermodynamic Bethe Ansatz and Generalised Hydrodynamics.

* Lenart Zadnik, Universite Paris-Saclay