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The anisotropic Heisenberg chain of spins 1/2 is one of the key paradigms of strongly correlated electrons in one dimension. While equilibrium properties of the model are relatively well understood, even very basic questions about its non-equilibrium properties were still open until very recently. A prominent example is the question whether the model exhibits ballistic spin transport at finite temperatures or not? I will outline the progress on this topic which has been triggered by the discovery of exact solution of quantum master equation of the boundary driven Heisenberg chain. The steady-state solution of non-equilibrium master equation leads to novel quasi-local conservation laws, which in turn lead to a derivation of rigorous strict lower bounds on ballistic transport coefficients. I will also explain how such an approach of `non-equilibrium integrability' works for some other strongly interacting quantum chains, for instance, for the Hubbard model or Lai- Sutherland model of spins 1.

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Tomaz Prosen, University of Ljubljana
Seminar Room TP 0.03
Contact: Vladislav Popkov