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arXiv · 2610.32710

Discrete WKB approach to density profiles in inhomogeneous two-band free-fermion chains

Federico Finkel·Artemio González-López·Martín Zapata
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Abstract

We extend the discrete WKB method to one-dimensional bipartite tight-binding chains of free fermions with slowly varying hopping amplitudes and on-site potentials. We focus on the inhomogeneous Rice-Mele model, suggesting possible experimental realizations thereof in optical superlattices. We derive explicit semiclassical expressions for the single-particle wave functions and density of states, as well as the sublattice-resolved local particle densities and filling fraction at arbitrary Fermi energy. In particular, we show that the WKB density profiles agree with those obtained from the local-density approximation. We analyze the spatial dependence of the local band edges and its consequences for the global spectral structure, and clarify the role played by the phase-space topology in determining the Bohr-Sommerfeld quantization conditions. Finally, we illustrate our results with two representative examples: a homogeneous Rice-Mele chain subject to a harmonic trap and a fully inhomogeneous chain containing a domain wall.

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Federico Finkel, Artemio González-López, Martín Zapata. 2026-10-23. Discrete WKB approach to density profiles in inhomogeneous two-band free-fermion chains. https://arxiv.org/abs/2610.32710

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