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Viernes 23 de marzo, 16 h Sala F12 Expositor: Tomaz Prosen Physics Department - University of Ljubljana - Ljubljana, Slovenia Abstract: We demonstrate a non-trivial exactly solvable case of the many-body Lindblad equation with strongly correlated bulk Hamiltonian (namely, the anisotropic Heisenberg spin 1/2 chain) and simple dissipation/decoherence (i.e. Lindblad) operators acting on the boundary two spins of the chain only. An exact ladder-tensor-network ansatz is presented [Phys. Rev. Lett. 107, 137201 (2011)] for non-equilibrium steady state of the open Heisenberg model in the far from equilibrium regime. We show that the steady-state density operator of a finite system of size n is -- apart from a normalization constant -- a polynomial of degree 2n-2 in the coupling constant. Efficient computation of physical observables is facilitated in terms of a transfer-operator reminiscent of a classical Markov process. In the isotropic case we find cosine spin profiles, 1/n^2 scaling of the spin current, and long-range correlations in the steady state. Furthermore, the perturbative (weak coupling) version of our ansatz [Phys. Rev. Lett. 106, 217206 (2011)] is used to derive a novel (Bethe Ansatz un-related) pseudo-local conservation law of the anisotropic Heisenberg model, by means of which we rigorously estimate (arXiv:1111.3830) the spin Drude weight (the ballistic transport coefficient) in the easy-plane regime. This closes a long standing question in strongly correlated condensed matter physics.
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