Reservoir-induced Thouless pumping and symmetry protected topological order in open quantum chains

Abstract

We introduce a classification scheme for symmetry protected topological phases applicable to stationary states of open systems based on a generalization of the many-body polarization. The polarization can be used to probe the topological properties of non-interacting and interacting closed and open systems as well and remains a meaningful quantity even in the presence of moderate particle-number fluctuations. As examples, we discuss two open-system versions of a topological Thouless pump in the steady state of one-dimensional lattices driven by Markovian reservoirs. In the analogous unitary system, the Rice-Mele model, symmetries enforce topological properties which lead to a non-trivial winding of the geometric Zak phase upon cyclic variations of model parameters. Associated with this is a winding of the many-body polarization, corresponding to a quantized transport in the bulk (Thouless pump). We here show that in the open system, where the Zak phase looses its meaning, the same symmetries enforce a winding of the generalized many- body polarization. This winding is shown to be robust against Hamiltonian perturbations as well as homogeneous dephasing and particle losses..

We have substantially rewritten the paper focusing more on the generality of our approach. For this we have also added a new model to show agreement to existing work. Because of this we have also added a new author

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