Abstract
Topological pumping and duality transformations are paradigmatic concepts in condensed matter and statistical mechanics. In this paper, we extend the concept of topological pumping of particles to topological pumping of quantum correlations. We propose a scheme to find pumping protocols for highly-correlated states by mapping them to uncorrelated ones. We show that one way to achieve this is to use dualities, because they are non-local transformations that preserve the topological properties of the system. By using them, we demonstrate that topological pumping of kinks and cluster-like excitations can be realized. We find that the entanglement of these highly-correlated excitations is strongly modified during the pumping process and the interactions enhance the robustness against disorder. Our work paves the way to explore topological pumping beyond the notion of particles and opens a new avenue to investigate the relation between correlations and topology.
Highlights
In 1983, Thouless demonstrated that the topological properties of the wave function of an extended system can be exploited to realize quantum pumps
We find that the entanglement of these highly correlated excitations is strongly modified during the pumping process and the interactions enhance the robustness against disorder
Our approach is based on a unitary transformation that maps correlated states to uncorrelated ones, where known protocols for topological pumping can be used
Summary
In 1983, Thouless demonstrated that the topological properties of the wave function of an extended system can be exploited to realize quantum pumps (see [1,2,3,4,5,6,7]) This mechanism can perform topologically protected quantum transport, which is robust against disorder and weak interactions [2]. While the duality can change the entanglement of the collective excitations [24,25], the topological properties of the energy bands are unaltered In this way, we can extend the idea of topological pumping to transport highly entangled excitations. We find that for a particular type of interaction topological pumping is still possible and, robustness against certain types of disorder is strongly enhanced
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