One-Particle Resonances and Eigenstate Thermalization in Periodic Free-Fermion Lattices
Abstract
We study eigenstate fluctuations of the particle number in the nearest-neighbour free-fermion model on the periodic cubic lattice (ℤ/Lℤ)d. For every fixed dimension, every particle number, every subvolume, and every normalized energy eigenstate, we prove a bound of order NLd−1 for the particle-number variance. The corresponding eigenstate-thermalization estimate is of order Ld−1/(Nη2) for fluctuations of relative size η. In particular, at positive particle density the bound decays as the inverse linear size. The proof decomposes the centered particle-number operator according to one-particle energy transfer and treats the zero- and nonzero-transfer components separately. The nonzero-transfer part is controlled by a sharp resonance bound, proved from Mann's theorem on relations among roots of unity, while the zero-transfer part is estimated by a Hilbert-Schmidt argument. These bounds are optimal in every dimension: the maximal nonzero-gap multiplicity has order Ld−1, and suitable many-body eigenstates realize matching variance lower bounds and show that the concentration bound cannot be improved in estimates uniform in the tolerance parameter.
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BibTeX
@misc{benoist2026oneparticle,
title = {{One-Particle Resonances and Eigenstate Thermalization in Periodic Free-Fermion Lattices}},
author = {Tristan Benoist and Vojkan Jakšić and Claude-Alain Pillet and Anna Szczepanek and Cornelia Vogel},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.12701},
eprint = {2611.12701},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.12701},
}
RIS
TY - UNPB
TI - One-Particle Resonances and Eigenstate Thermalization in Periodic Free-Fermion Lattices
AU - Tristan Benoist
AU - Vojkan Jakšić
AU - Claude-Alain Pillet
AU - Anna Szczepanek
AU - Cornelia Vogel
PY - 2026
DA - 2026/11/09
PB - arXiv
DO - 10.48550/arxiv.2611.12701
UR - https://arxiv.org/abs/2611.12701
AB - We study eigenstate fluctuations of the particle number in the nearest-neighbour free-fermion model on the periodic cubic lattice (ℤ/Lℤ)^d. For every fixed dimension, every particle number, every subvolume, and every normalized energy eigenstate, we prove a bound of order NL^d−1 for the particle-number variance. The corresponding eigenstate-thermalization estimate is of order L^d−1/(Nη^2) for fluctuations of relative size η. In particular, at positive particle density the bound decays as the inverse linear size. The proof decomposes the centered particle-number operator according to one-particle energy transfer and treats the zero- and nonzero-transfer components separately. The nonzero-transfer part is controlled by a sharp resonance bound, proved from Mann's theorem on relations among roots of unity, while the zero-transfer part is estimated by a Hilbert-Schmidt argument. These bounds are optimal in every dimension: the maximal nonzero-gap multiplicity has order L^d−1, and suitable many-body eigenstates realize matching variance lower bounds and show that the concentration bound cannot be improved in estimates uniform in the tolerance parameter.
ER -