Discrete WKB approach to density profiles in inhomogeneous two-band free-fermion chains
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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BibTeX
@misc{finkel2026discrete,
title = {{Discrete WKB approach to density profiles in inhomogeneous two-band free-fermion chains}},
author = {Federico Finkel and Artemio González-López and Martín Zapata},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32710},
eprint = {2610.32710},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32710},
}
RIS
TY - UNPB
TI - Discrete WKB approach to density profiles in inhomogeneous two-band free-fermion chains
AU - Federico Finkel
AU - Artemio González-López
AU - Martín Zapata
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32710
UR - https://arxiv.org/abs/2610.32710
AB - 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.
ER -