The Geometry of Lee-Yang Tensors
Abstract
We provide a geometric description of Lee-Yang tensors, building upon several recent results of Bravyi, Gosset, Liu, and Wong. By applying tools from complex Perron-Frobenius theory, we generalize one of their key lemmas to bound the spectral ratio of non-normal operators with Lee-Yang radius greater than one. As a direct consequence, we provide a local-to-global principle for bounding spectral gaps of Suzuki-Fisher Hamiltonians, a family of $2$-local Hamiltonians, using only the Lee-Yang radius of each local operator to bound the gap from below. On the other hand, we develop a simple perturbative technique to show that the Gibbs states of k-local Hamiltonians, k ≥ 3, cannot have Lee-Yang radius at least one for all inverse temperatures β≥ 0. We apply this same method to conclude that Suzuki-Fisher Hamiltonians are precisely those Hamiltonians whose Gibbs states are Lee-Yang at all inverse temperatures β≥ 0.
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BibTeX
@misc{hofgard2026geometry,
title = {{The Geometry of Lee-Yang Tensors}},
author = {Jake Hofgard},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.09485},
eprint = {2610.09485},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.09485},
}
RIS
TY - UNPB
TI - The Geometry of Lee-Yang Tensors
AU - Jake Hofgard
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.09485
UR - https://arxiv.org/abs/2610.09485
AB - We provide a geometric description of Lee-Yang tensors, building upon several recent results of Bravyi, Gosset, Liu, and Wong. By applying tools from complex Perron-Frobenius theory, we generalize one of their key lemmas to bound the spectral ratio of non-normal operators with Lee-Yang radius greater than one. As a direct consequence, we provide a local-to-global principle for bounding spectral gaps of Suzuki-Fisher Hamiltonians, a family of $2$-local Hamiltonians, using only the Lee-Yang radius of each local operator to bound the gap from below. On the other hand, we develop a simple perturbative technique to show that the Gibbs states of k-local Hamiltonians, k ≥ 3, cannot have Lee-Yang radius at least one for all inverse temperatures β≥ 0. We apply this same method to conclude that Suzuki-Fisher Hamiltonians are precisely those Hamiltonians whose Gibbs states are Lee-Yang at all inverse temperatures β≥ 0.
ER -