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.
Highlights
The modelWe consider a bosonic system on a one-dimensional lattice described by the following Hamiltonian,
In this work, we take advantage of the flexibility that cold-atomic systems offer and show that, apart from their role as quantum simulators of solid-state systems, they can be used to explore novel strongly-correlated phenomena beyond those found in natural materials
Our work show the possibilities that ultracold atomic systems offer to investigate strongly-correlated topological phenomena beyond those found in natural materials
Summary
We consider a bosonic system on a one-dimensional lattice described by the following Hamiltonian,. This model possesses a U(1) × U(1) symmetry corresponding to the conservation of total particle number N = i〈ni〉 and magnetization M = i〈σzi 〉. The interplay between these two conserved quantities will be crucial, as we shall see, to describe the different phases of the model. In such a setting, the bosons are strongly repulsive and the XXZ Hamiltonian favors Néel order in the spins. We fix α = 0.5t throughout the paper and consider bosonic densities ρ = N /L ≤ 1.
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