Devil's staircase of topological Peierls insulators and Peierls supersolids

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.

24 pages, 9 figures. Close to published version

References in corpus (14)

• Many-Body Physics with Ultracold Gases
• Observation of the supersolid stripe phase in spin-orbit coupled Bose-Einstein condensates
• Transient supersolid properties in an array of dipolar quantum droplets
• Non-standard Hubbard models in optical lattices: a review
• Spin transport in a tunable Heisenberg model realized with ultracold atoms
• Realizing a scalable building block of a U(1) gauge theory with cold atomic mixtures
• Hidden order in 1D Bose insulators
• Detecting Chiral Edge States in the Hofstadter Optical Lattice
• Two-Stage Melting in Systems of Strongly Interacting Rydberg Atoms
• Supersolid Bose-Fermi Mixtures in Optical Lattices
• Dynamical solitons and boson fractionalization in cold-atom topological insulators
• Dynamical creation of a supersolid in asymmetric mixtures of bosons
• ${\mathbb{Z}}_n$ solitons in intertwined topological phases
• Floating Phases in One-Dimensional Rydberg Ising Chains