Devil's staircase of topological Peierls insulators and Peierls supersolids

TL;DR

This paper explores how ultracold bosonic atoms in a one-dimensional lattice can exhibit a rich variety of topological phases and supersolid states due to a bosonic analog of the Peierls mechanism, revealing new strongly-correlated phenomena.

Contribution

It demonstrates the emergence of a Devil's staircase of topological phases and supersolids in a bosonic system with spin-dependent tunneling and antiferromagnetic interactions.

Findings

Discovery of a Devil's staircase of symmetry-protected topological phases.

Identification of Peierls supersolids without long-range interactions.

Observation of coexistence of long-range order and topological properties.

Abstract

We consider a mixture of ultracold bosonic atoms on a one-dimensional lattice described by the XXZ-Bose-Hubbard model, where the tunneling of one species depends on the spin state of a second deeply trapped species. We show how the inclusion of antiferromagnetic interactions among the spin degrees of freedom generates a Devil's staircase of symmetry-protected topological phases for a wide parameter regime via a bosonic analog of the Peierls mechanism in electron-phonon systems. These topological Peierls insulators are examples of symmetry-breaking topological phases, where long-range order due to spontaneous symmetry breaking coexists with topological properties such as fractionalized edge states. Moreover, we identify a region of supersolid phases that do not require long-range interactions. They appear instead due to a Peierls incommensurability mechanism, where competing orders modify the underlying crystalline structure of Peierls insulators, becoming superfluid. Our work show the possibilities that ultracold atomic systems offer to investigate strongly-correlated topological phenomena beyond those found in natural materials.