Topological phases in odd-legs frustrated synthetic ladders

Abstract

The realization of the Hofstadter model in a strongly anisotropic ladder geometry has now become possible in one-dimensional optical lattices with a synthetic dimension. In this work, we show how the Hofstadter Hamiltonian in such ladder configurations hosts a topological phase of matter which is radically different from its two-dimensional counterpart. This topological phase stems directly from the hybrid nature of the ladder geometry, and is protected by a properly defined inversion symmetry. We start our analysis considering the paradigmatic case of a three-leg ladder which supports a topological phase exhibiting the typical features of topological states in one dimension: robust fermionic edge modes, a degenerate entanglement spectrum and a non-zero Zak phase; then, we generalize our findings - addressable in the state-of-the-art cold atom experiments - to ladders with an higher number of legs.

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Cited by in corpus (15)

• Topological quantum matter with cold atoms
• Band Gap Closing in a Synthetic Hall Tube of Neutral Fermions
• Tunable Flux through a Synthetic Hall Tube of Neutral Fermions
• Enhancement of chiral edge currents in ($d$+1)-dimensional atomic Mott-band hybrid insulators
• Stückelberg interferometry using spin-orbit-coupled cold atoms in an optical lattice
• Topological Devil's staircase in atomic two-leg ladders
• Synthetic Hall ladder with tunable magnetic flux
• Topological chiral currents in the Gross-Neveu model extension
• Spectrum, Lifshitz transitions and orbital currents in frustrated fermionic ladders with a uniform flux
• Exploring helical phases of matter in bosonic ladders
• Emergence of non-Abelian SU(2) invariance in Abelian frustrated fermionic ladders
• Synthetic Hall tube of interacting fermions
• Frustrated mixed-spin ladders: Evidence for a bond order wave phase between rung-singlet and Haldane phases
• The large $|U|$ expansion for a half-filled asymmetric Hubbard model on a triangular ladder in the presence of spin-dependent magnetic flux
• Quantum States and Spectra of Small Cylindrical and Toroidal Lattices