Topological Devil's staircase in atomic two-leg ladders

Abstract

We show that a hierarchy of topological phases in one dimension -- a topological Devil's staircase -- can emerge at fractional filling fractions in interacting systems, whose single-particle band structure describes a topological or a crystalline topological insulator. Focusing on a specific example in the BDI class, we present a field-theoretical argument based on bosonization that indicates how the system, as a function of the filling fraction, hosts a series of density waves. Subsequently, based on a numerical investigation of the low-lying energy spectrum, Wilczek-Zee phases, and entanglement spectra, we show that they are symmetry protected topological phases. In sharp contrast to the non-interacting limit, these topological density waves do not follow the bulk-edge correspondence, as their edge modes are gapped. We then discuss how these results are immediately applicable to models in the AIII class, and to crystalline topological insulators protected by inversion symmetry. Our findings are immediately relevant to cold atom experiments with alkaline-earth atoms in optical lattices, where the band structure properties we exploit have been recently realized.

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• Topological Creutz Ladder in a Resonantly Shaken 1D Optical Lattice
• Many-Body Flatband Localization
• Extended flat-bands, entanglement and topological properties in a Creutz ladder
• Interaction induced doublons and embedded topological subspace in a complete flat-band system
• Non-thermalized Dynamics of Flat-Band Many-Body Localization
• Interacting second-order topological insulators in one-dimensional fermions with correlated hopping
• Exact projector Hamiltonian, local integrals of motion, and many-body localization with topological order
• Topological Floquet engineering of a 1D optical lattice via resonantly shaking with two harmonic frequencies
• Exploring helical phases of matter in bosonic ladders
• Flat-band full localization and symmetry-protected topological phase on bilayer lattice systems
• Cold atoms meet lattice gauge theory
• Tunable zero modes and quantum interferences in flat-band topological insulators