Interacting Electronic Topology of Nonlocal Crystals

TL;DR

This paper explores how nonlocal interactions in crystals can give rise to new topological phases, extending the understanding of topological matter beyond local interaction models.

Contribution

It introduces a novel topological phase in one-dimensional nonlocal crystals with symmetry protection, demonstrated through a specific fermionic model.

Findings

Discovery of a new topological phase in nonlocal crystals

Construction of a topological charge pump as a physical signature

Identification of the phase via symmetry eigenvalues

Abstract

Nonlocal crystals are systems with translational symmetry but arbitrary range couplings or interactions between degrees of freedom. We argue that the notion of topology in such systems does not collapse to that in zero dimensions, as one may naively expect in view of the infinite interaction range. At the same time, we show that the range of available topological phases can be enriched in comparison to the case with local interactions. This is demonstrated by constructing an example of a fermionic symmetry-protected phase in one dimension in symmetry class AII with inversion symmetry, using a Hatsugai-Kohmoto-type model. The new phase exists only in a nonlocal crystal with electron-electron interactions and can be identified from symmetry eigenvalues. We construct an associated topological charge pump as a physical manifestation of its topology.