Breakdown of the Peierls substitution for the Haldane model with ultracold atoms

Julen Ibañez-Azpiroz, Asier Eiguren, Aitor Bergara, Giulio Pettini, and Michele Modugno
Phys. Rev. A 90, 033609 – Published 8 September 2014

Abstract

We present two independent approaches for calculating the tight-binding parameters of the Haldane model with ultracold atoms. The tunneling coefficients up to next-nearest neighbors are computed ab initio by using the maximally localized Wannier functions and compared to analytical expressions written in terms of gauge-invariant measurable properties of the spectrum. The two approaches present a remarkable agreement and evidence the breakdown of the Peierls substitution: (i) the phase acquired by the next-nearest tunneling amplitude t1 presents quantitative and qualitative differences with respect to that obtained by the integral of the vector field A, as considered in the Peierls substitution, even in the regime of low amplitudes of A; and (ii) for larger values, also |t1| and the nearest-neighbor tunneling t0 have a marked dependence on A. The origin of this behavior and its implications are discussed.

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  • Received 15 May 2014

DOI:https://doi.org/10.1103/PhysRevA.90.033609

©2014 American Physical Society

Authors & Affiliations

Julen Ibañez-Azpiroz1, Asier Eiguren2,3, Aitor Bergara2,3,4, Giulio Pettini5, and Michele Modugno6,7

  • 1Peter Grünberg Institute and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, D-52425 Jülich, Germany
  • 2Departamento de Física de la Materia Condensada, Universidad del Pais Vasco, UPV/EHU, 48080 Bilbao, Spain
  • 3Donostia International Physics Center, 20018 Donostia, Spain
  • 4Centro de Física de Materiales, Centro Mixto CSIC-UPV/EHU, 20018 Donostia, Spain
  • 5Dipartimento di Fisica e Astronomia, Università di Firenze and INFN, 50019 Sesto Fiorentino, Italy
  • 6Departamento de Física Teórica e Histórico de la Ciencia, Universidad del Pais Vasco, UPV/EHU, 48080 Bilbao, Spain
  • 7Ikerbasque, Basque Foundation for Science, 48011 Bilbao, Spain

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Issue

Vol. 90, Iss. 3 — September 2014

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