We present an identification of the spectra of local conserved operators of integrable quantum lattice models and the density distributions of their thermodynamic particle content. This is derived explicitly for the Heisenberg XXZ spin chain. As an application we discuss a quantum quench scenario, in both the gapped and critical regimes. We outline an exact technique which allows for an efficient implementation on periodic matrix product states. In addition, for certain simple product states we obtain closed-form expressions for the density distributions in terms of solutions to Hirota difference equations. Remarkably, no reference to a maximal entropy principle is invoked.ArXiv ePrint: 1512.04454
We argue that a particle language provides a conceptually simple framework for the description of anomalous equilibration in isolated quantum systems. We address this paradigm in the context of integrable models, which are those with particles that are stable against decay. In particular, we demonstrate that a complete description of equilibrium ensembles for interacting integrable models requires a formulation built from the mode occupation numbers of the underlying particle content, mirroring the case of non-interacting particles. This yields an intuitive physical interpretation of generalized Gibbs ensembles, and reconciles them with the microcanonical ensemble. We explain how previous attempts to identify an appropriate ensemble overlooked an essential piece of information, and provide explicit examples in the context of quantum quenches.
We consider two lattice models for strongly correlated electrons which are exactlysolvable in one dimension. Along with the Hubbard model and the su(2|2) spin chain, these are the only parity-invariant models that can be obtained from Shastry's R-matrix. One exhibits itinerant ferromagnetic behaviour, while for the other the electrons form bound pairs and at half-filling the model becomes insulating. We derive the TBA equations for the models, analyze them at various limits, and in particular obtain zero temperature phase diagrams. Furthermore we consider extensions of the models, which reduce to the Essler-Korepin-Schoutens model in certain limits.
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