Devil’s staircase of topological Peierls insulators and Peierls supersolids

Authors: Chanda, Titas; Gonzalez-Cuadra, Daniel; Lewenstein, Maciej; Tagliacozzo, Luca; Zakrzewski, Jakub

Journal: SCIPOST PHYSICS

Publication date: 2022/02/01

DOI: 10.21468/SciPostPhys.12.2.076

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 antiferro-magnetic 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.