# Devil's staircase of topological Peierls insulators and Peierls supersolids

### Submission summary

 As Contributors: Titas Chanda · Jakub Zakrzewski Arxiv Link: https://arxiv.org/abs/2011.09228v4 (pdf) Date submitted: 2021-09-03 10:02 Submitted by: Chanda, Titas Submitted to: SciPost Physics Academic field: Physics Specialties: Atomic, Molecular and Optical Physics - Theory Condensed Matter Physics - Theory Quantum Physics Approach: Theoretical

### 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.

###### Current status:
Editor-in-charge assigned

### List of changes

1. We now show that the off-diagonal correlations $\langle{\hat{b}^{\dagger}_j \hat{b}_{j+R}}\rangle$ decay exponentially with the distance $R$ (Fig. 3 (a) in the updated manuscript) in the commensurate Peierls insulators confirming their insulating nature.

2. The evidence of the existence of diagonal long-range order in the Peierls insulators has been provided by showing that the peak in the structure factor $S_{\sigma}(k)$ remains finite in the thermodynamic limit (Fig. 3 (b) in the updated manuscript).

3. Following Referee’s suggestion, we now refrain from using the term ‘staircase’ when describing the region of Peierls supersolids as this region is compressible and thus the steps in terms of bosonic density $\rho$ vanish in the thermodynamic limit.