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

Abstract

We present two independent calculations of the tight-binding parameters for a specific realization of the Haldane model with ultracold atoms. The tunneling coefficients up to next-to-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-to-nearest tunneling amplitude $t_1$ 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; (ii) for larger values, also $|t_1|$ and the nearest-neighbor tunneling $t_0$ have a marked dependence on A. The origin of this behavior and its implications are discussed.

5 pages, 5 figures

References in corpus (7)

• Tunable gauge potential for neutral and spinless particles in driven lattices
• Non-Abelian gauge fields and topological insulators in shaken optical lattices
• Non-Abelian optical lattices: Anomalous quantum Hall effect and Dirac Fermions
• Realizing and Detecting the Haldane's Quantum Hall effect with Ultracold Atoms
• Ultracold Fermions in a Graphene-Type Optical Lattice
• Topological Insulators and Metals in Atomic Optical Lattices
• Time-of-flight patterns of ultra-cold bosons in optical lattices in various Abelian artificial magnetic field gauges

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• Hofstadter spectrum of Chern bands in twisted transition metal dichalcogenides
• Shift photoconductivity in the Haldane model
• Correspondence between a shaken honeycomb lattice and the Haldane model
• Insights into the orbital magnetism of noncollinear magnetic systems