Interacting Topological Insulators with Synthetic Dimensions

TL;DR

This paper explores how interactions in synthetic dimension topological insulators differ from traditional systems, revealing that such interactions can alter the topological classification in unexpected ways.

Contribution

It demonstrates that generic interactions in synthetic topological insulators are qualitatively different and can modify their topological classification, unlike local interactions in conventional systems.

Findings

Interactions in synthetic topological insulators differ from local interactions.

Such interactions can change the topological classification.

Synthetic techniques accurately simulate high-dimensional band structures.

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.