2018/10/31 by S Barbarino, S. Barbarino, D. Rossini +9 · 1 citation
Materials Science · Physics and Astronomy · #Bosonization #Chemical and Physical Properties of Materials #Quantum many-body systems #Symmetry (geometry) #Symmetry protected topological order #Topological Materials and Phenomena #Topological entropy in physics #Topological insulator #Topological order #Topological quantum number #Topology (electrical circuits) #cond-mat.quant-gas
paper · pdf · doi:10.1088/1367-2630/ab0e18
published as New J. Phys. 21, 043048 (2019)
openalex created_date 2018/10/12 · openalex publication_date 2019/03/08 · arxiv created 2019/05/06 · arxiv updated 2019/05/22 · openalex updated_date 2026/08/05
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.