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.

Topological Devil's staircase in atomic two-leg ladders / Barbarino, S.; Rossini, D.; Rizzi, M.; Fazio, R.; Santoro, G. E.; Dalmonte, Marcello. - In: NEW JOURNAL OF PHYSICS. - ISSN 1367-2630. - 21:4(2019), pp. 1-16. [10.1088/1367-2630/ab0e18]

Topological Devil's staircase in atomic two-leg ladders

Barbarino S.
;
Rizzi M.;Santoro G. E.;Dalmonte, Marcello
2019

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.
21
4
1
16
043048
https://iopscience.iop.org/article/10.1088/1367-2630/ab0e18/pdf
Barbarino, S.; Rossini, D.; Rizzi, M.; Fazio, R.; Santoro, G. E.; Dalmonte, Marcello
File in questo prodotto:
File Dimensione Formato  
Barbarino_NJP19.pdf

accesso aperto

Descrizione: Open Access article
Tipologia: Versione Editoriale (PDF)
Licenza: Creative commons
Dimensione 1.19 MB
Formato Adobe PDF
1.19 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11767/98408
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 11
  • ???jsp.display-item.citation.isi??? 12
social impact