| dc.description.abstract | 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. In the setting of quantum
many-body systems on a lattice it is natural to consider Lindbladians that decompose
into a sum of local interactions with decreasing strength with respect to
the size of their support. For both practical and theoretical reasons, it is crucial
to estimate the impact that perturbations in the generating Lindbladian, arising
as noise or errors, can have on the evolution. These local perturbations are potentially
unbounded, but constrained to respect the underlying lattice structure.
We show that even for polynomially decaying errors in the Lindbladian, local
observables and correlation functions are stable if the unperturbed Lindbladian
has a unique fixed point and a mixing time which scales logarithmically with
the system size. The proof relies on Lieb-Robinson bounds, which describe a
finite group velocity for propagation of information in local systems. As a main
example, we prove that classical Glauber dynamics is stable under local perturbations,
including perturbations in the transition rates which may not preserve
detailed balance. | |
