Matrix Product Ansatz for nonequilibrium steady states of driven quantum systems

by Vladislav Popkov (University of Cologne and CSDC, Universita di Firenze)

Monday 3 Nov 2014, 14:30 → 16:00 Europe/Rome

Aula Rasetti (Dip. di Fisica - Edificio G. Marconi)

We review recent developments, concerning one-dimensional open quantum systems, connected at the ends to dissipative baths, which sustain global gradients of magnetization and energy across the system. A quantum Master equation in the Lindblad form, describing a time evolution of a reduced density matrix, has a fixed point, for which an exact solution in the form of a Matrix Product Ansatz can be written, for several well-known integrable models. Consistency condititions define algebraic relations for the auxiliary operators, which are related to a bulk symmetry of the Hamiltonian. Nonequilibrium quantum steady state, including scaling limit, can thus be investigated, which is illustrated on an example of a driven XXX Heisenberg spin chain with boundary reservoirs targeting different boundary polarizazions. A transfer matrix of the problem has an underlying Yang-Baxter structure, which hints at the full integrability of the Liouvillean dynamics.