The realization of the Hofstadter model in a strongly anisotropic ladder geometry has now become possible in one-dimensional optical lattices with a synthetic dimension. In this work, we show how the Hofstadter Hamiltonian in such ladder configurations hosts a topological phase of matter which is radically different from its two-dimensional counterpart. This topological phase stems directly from the hybrid nature of the ladder geometry and is protected by a properly defined inversion symmetry. We start our analysis by considering the paradigmatic case of a three-leg ladder which supports a topological phase exhibiting the typical features of topological states in one dimension: robust fermionic edge modes, a degenerate entanglement spectrum, and a nonzero Zak phase; then, we generalize our findings - addressable in the state-of-the-art cold-atom experiments - to ladders with a higher number of legs.

Topological phases in frustrated synthetic ladders with an odd number of legs / Barbarino, Simone; Dalmonte, Marcello; Fazio, Rosario; Santoro, Giuseppe E.. - In: PHYSICAL REVIEW. A. - ISSN 2469-9934. - 97:1(2018), pp. 1-7. [10.1103/PhysRevA.97.013634]

Topological phases in frustrated synthetic ladders with an odd number of legs

Barbarino, Simone
;
Dalmonte, Marcello;Santoro, Giuseppe E.
2018

Abstract

The realization of the Hofstadter model in a strongly anisotropic ladder geometry has now become possible in one-dimensional optical lattices with a synthetic dimension. In this work, we show how the Hofstadter Hamiltonian in such ladder configurations hosts a topological phase of matter which is radically different from its two-dimensional counterpart. This topological phase stems directly from the hybrid nature of the ladder geometry and is protected by a properly defined inversion symmetry. We start our analysis by considering the paradigmatic case of a three-leg ladder which supports a topological phase exhibiting the typical features of topological states in one dimension: robust fermionic edge modes, a degenerate entanglement spectrum, and a nonzero Zak phase; then, we generalize our findings - addressable in the state-of-the-art cold-atom experiments - to ladders with a higher number of legs.
97
1
1
7
013634
https://journals.aps.org/pra/abstract/10.1103/PhysRevA.97.013634
https://arxiv.org/abs/1708.02929
Barbarino, Simone; Dalmonte, Marcello; Fazio, Rosario; Santoro, Giuseppe E.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11767/87925
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