Seminar

Stability of local quantum dissipative systems

By
Angelo Lucía (Universidad Complutense de Madrid)
Date
Place
Universitat de Barcelona, Facultat de Física, 5th Floor (old building), sala Pere Pascual.
seminar ICCUB
Open quantum systems weakly coupled to the environment are modeled by completely positive, trace preserving semigroups of linear maps. The generators of such evolutions are called Lindbladians. For both practical and theoretical reasons, it is crucial to estimate the impact that noise or errors in the generating Lindbladian can have on the evolution. In the setting of quantum many-body systems on a lattice it is natural to consider local or exponentially decaying interactions. We show that in this case local observables and correlation functions are stable if the Lindbladian is frustration-free, translational invariant, has a unique fixed point (with no restriction on its rank) and has a mixing time which scales logarithmically with the system size. These conditions can be relaxed to the non-translational invariant case, at the cost of requiring Local Topological Quantum Order. As a main example we prove that classical Glauber dynamics (in the regime where mixes fast enough) is stable under local perturbations, including perturbations in the transition rates which do not preserve detailed balance. To our knowledge, this result is new even classically.