Topological edge states and quantized transport in unitary and dissipative one-dimensional lattice models
Prof. Dr. Michael Fleischhauer (Fachbereich Physik, Universität Kaiserslautern)

I discuss bosonic atoms in a one-dimensional superlattice potential with alter- nating tunneling rates t1 and t2 and with on-site [1] and non-local interactions. This model is the bosonic analogue of the Su-Schrieffer-Heeger model, which possesses topological properties in the half-filling Mott insulating (MI) phase. I introduce a many-body topological invariant, and discuss the emergence of edge states as well as a quantized topological transport in the bulk. Due to the absence of particle-hole symmetry the bulk-boundary correspondence, known from the fermionic model needs to be generalized. In the presence of non-local interactions topologically non-trivial phases with fractional filling are identified. In the second part of the talk I discuss an open 1D spin chain, described by a Lindblad master equation. This model is shown to have a quantized bulk transport, allowing for the definition of a topological invariant of the Liouvillian in terms of a measurable quantity. The invariant is shown to be robust against unitary perturbations as well as decoherence and dissipation.

[1] F. Grusdt, M. Hoening, and M. Fleischhauer, Phys. Rev. Lett. 110, 260405 (2013).

[2] D. Linzner, M. Koster and M. Fleischhauer, (in preparation)