Interacting Topological Insulators with Synthetic Dimensions

Abstract

Recent developments of experimental techniques have given us unprecedented opportunities of studying topological insulators in high dimensions, while some of the dimensions are "synthetic", in the sense that the effective lattice momenta along these synthetic dimensions are controllable periodic tuning parameters. In this work, we study interaction effects on topological insulators with synthetic dimensions. We show that although the free fermion band structure of high dimensional topological insulators can be precisely simulated with the "synthetic techniques", the generic interactions in these effective synthetic topological insulators are qualitatively different from the local interactions in ordinary condensed matter systems. And we show that these special but generic interactions have unexpected effects on topological insulators, namely they would change (or reduce) the classification of topological insulators differently from the previously extensively studied local interactions.

9 pages and 3 figures

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Cited by in corpus (8)

• Dropping an impurity into a Chern insulator: a polaron view on topological matter
• Generalized Wen-Zee Terms
• Fracton physics of spatially extended excitations
• Reduction of one-dimensional non-Hermitian point-gap topology by correlations
• Fate of exceptional points under interactions: Reduction of topological classifications
• Polaron in a $p+ip$ Fermi topological superfluid
• Weyl singularities in polaritonic multi-terminal Josephson junctions
• Definition and Classification of Fermi Surface Anomalies