Viernes 23 de marzo, 16 h
Expositor: Tomaz Prosen
Physics Department - University of Ljubljana -
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.