Topological Devil’s staircase in atomic two-leg ladders
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 th...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2019-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/ab0e18 |
| _version_ | 1797749977614647296 |
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| author | S Barbarino D Rossini M Rizzi R Fazio G E Santoro M Dalmonte |
| author_facet | S Barbarino D Rossini M Rizzi R Fazio G E Santoro M Dalmonte |
| author_sort | S Barbarino |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-12T16:27:22Z |
| format | Article |
| id | doaj.art-4d202c3badd4454dba6ad510a900e312 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:27:22Z |
| publishDate | 2019-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-4d202c3badd4454dba6ad510a900e3122023-08-08T15:40:15ZengIOP PublishingNew Journal of Physics1367-26302019-01-0121404304810.1088/1367-2630/ab0e18Topological Devil’s staircase in atomic two-leg laddersS Barbarino0D Rossini1https://orcid.org/0000-0002-9222-1913M Rizzi2R Fazio3G E Santoro4M Dalmonte5Scuola Internazionale Studi Superiori Avanzati (SISSA) , Via Bonomea 265, I-34136, Trieste, Italy; Institute of Theoretical Physics, Technische Universität Dresden , D-01062, Dresden, GermanyDipartimento di Fisica, Università di Pisa and INFN , Largo Pontecorvo 3, I-56127, Pisa, ItalyInstitute für Physik, Johannes Gutenberg-Universität , D-55128, Mainz, Germany; Institute of Quantum Control (PGI-8) , Forschungszentrum Jülich, D-52425, Jülich, Germany; Institute for Theoretical Physics, University of Cologne , D-50937, Köln, GermanyInternational Centre for Theoretical Physics (ICTP) , PO Box 586, I-34014, Trieste, Italy; NEST, Scuola Normale Superiore & Istituto Nanoscienze-CNR , I-56126, Pisa, ItalyScuola Internazionale Studi Superiori Avanzati (SISSA) , Via Bonomea 265, I-34136, Trieste, Italy; NEST, Scuola Normale Superiore & Istituto Nanoscienze-CNR , I-56126, Pisa, Italy; CNR-IOM Democritos National Simulation Center , Via Bonomea 265, I-34136, Trieste, ItalyScuola Internazionale Studi Superiori Avanzati (SISSA) , Via Bonomea 265, I-34136, Trieste, Italy; International Centre for Theoretical Physics (ICTP) , PO Box 586, I-34014, Trieste, ItalyWe 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.https://doi.org/10.1088/1367-2630/ab0e18fractional topological phasetwo-leg ladderstrongly correlatedcold-atoms |
| spellingShingle | S Barbarino D Rossini M Rizzi R Fazio G E Santoro M Dalmonte Topological Devil’s staircase in atomic two-leg ladders New Journal of Physics fractional topological phase two-leg ladder strongly correlated cold-atoms |
| title | Topological Devil’s staircase in atomic two-leg ladders |
| title_full | Topological Devil’s staircase in atomic two-leg ladders |
| title_fullStr | Topological Devil’s staircase in atomic two-leg ladders |
| title_full_unstemmed | Topological Devil’s staircase in atomic two-leg ladders |
| title_short | Topological Devil’s staircase in atomic two-leg ladders |
| title_sort | topological devil s staircase in atomic two leg ladders |
| topic | fractional topological phase two-leg ladder strongly correlated cold-atoms |
| url | https://doi.org/10.1088/1367-2630/ab0e18 |
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