Bulk gap stability and spectral flow for fermions with weak long-range interactions
Abstract
We prove that weak long-range many-body interactions preserve the bulk gap of a free fermion system and that a quasi-local spectral flow transports the free ground state to ground states of the interacting system. Let Φh be a free fermionic interaction, possibly including pairing terms, whose infinite-volume Majorana coefficient operator h has no spectrum in (−g,g), and let 𝒱 be an even self-adjoint many-body interaction. For sufficiently small |λ|, we construct pure ground states ωλ of the interacting bulk system Φλ=Φh+λ𝒱 and quasi-local automorphisms β0,λ such that ωλ=ω0∘β0,λ, where ω0 is the free ground state of Φh. Each ωλ has a GNS Hamiltonian with gap at least g−C*|λ| |𝒱|*, where |·|* is the relevant interaction norm. Our result allows polynomial decay of both the free coefficients and the many-body interaction. For two-site interactions on a uniformly discrete point set Γ⊂ℝd, a sufficient condition is decay as (1+|x−y|)−ϖ with ϖ>2d, for both the hopping and pairing coefficients and the interaction terms. The spectral-flow generator preserves the spatial exponent of the polynomial interaction norm, and its automorphisms satisfy locality bounds at that exponent. If h and 𝒱 have stretched-exponential decay, so does the spectral-flow generator. The proof constructs the spectral flow and establishes the gap through an excitation-number comparison, using polynomial propagation bounds for evolved interactions proved in a companion paper.
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BibTeX
@misc{teufel2026bulk,
title = {{Bulk gap stability and spectral flow for fermions with weak long-range interactions}},
author = {Stefan Teufel},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40299},
eprint = {2610.40299},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40299},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Bulk gap stability and spectral flow for fermions with weak long-range interactions
AU - Stefan Teufel
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40299
UR - https://arxiv.org/abs/2610.40299
AB - We prove that weak long-range many-body interactions preserve the bulk gap of a free fermion system and that a quasi-local spectral flow transports the free ground state to ground states of the interacting system. Let Φ_h be a free fermionic interaction, possibly including pairing terms, whose infinite-volume Majorana coefficient operator h has no spectrum in (−g,g), and let 𝒱 be an even self-adjoint many-body interaction. For sufficiently small |λ|, we construct pure ground states ω_λ of the interacting bulk system Φ_λ=Φ_h+λ𝒱 and quasi-local automorphisms β_0,λ such that ω_λ=ω_0∘β_0,λ, where ω_0 is the free ground state of Φ_h. Each ω_λ has a GNS Hamiltonian with gap at least g−C_*|λ| |𝒱|_*, where |·|_* is the relevant interaction norm. Our result allows polynomial decay of both the free coefficients and the many-body interaction. For two-site interactions on a uniformly discrete point set Γ⊂ℝ^d, a sufficient condition is decay as (1+|x−y|)^−ϖ with ϖ>2d, for both the hopping and pairing coefficients and the interaction terms. The spectral-flow generator preserves the spatial exponent of the polynomial interaction norm, and its automorphisms satisfy locality bounds at that exponent. If h and 𝒱 have stretched-exponential decay, so does the spectral-flow generator. The proof constructs the spectral flow and establishes the gap through an excitation-number comparison, using polynomial propagation bounds for evolved interactions proved in a companion paper.
ER -