Regensburg 2019 – scientific programme
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TT: Fachverband Tiefe Temperaturen
TT 3: Topological Insulators (joint session TT/MA)
TT 3.13: Talk
Monday, April 1, 2019, 12:45–13:00, Theater
Topological Devil's staircase in atomic two-leg ladders — Simone Barbarino1,2, Davide Rossini3, •Matteo Rizzi4, Rosario Fazio5,6, Giuseppe E. Santoro1,5,7, and Marcello Dalmonte1,5 — 1SISSA, Trieste, Italy — 2Technische Universität Dresden, Germany — 3Università di Pisa and INFN, Italy — 4Johannes Gutenberg- Universität, Mainz, Germany — 5ICTP, Trieste, Italy — 6NEST, SNS & Istituto Nanoscienze-CNR, Pisa, Italy — 7CNR-IOM Democritos, Trieste, Italy
We show that a hierarchy of symmetry-protected topological (SPT) phases in 1D --a topological Devil's staircase -- can emerge at fractional filling fractions in interacting systems, whose single-particle band structure describes 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 phase diagram, as a function of the filling fraction, hosts a series of density waves. Subsequently, based on a numerical investigation of spectral properties, Wilczek-Zee phases, and entanglement spectra, we show that these phases can support SPT order. In sharp contrast to the non-interacting limit, these topological density waves do not follow the boundary-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.