Gaussian-Bond Hall Viscosity and Nonlocal Hall Response of a Sampled Landau Level
Abstract
Hall viscosity on a lattice depends on how strain changes microscopic hopping amplitudes. For a specified Gaussian envelope, bond-length derivatives close on the undeformed hopping, expressing the stress as an embedded momentum Hessian and relating the viscosity to higher-order band geometry. In the Kapit--Mueller parent family at rational flux, we show that the stress response equals the strain curvature of the sampled-LLL Gram matrix. The density-normalized viscosity approaches the continuum value 1/4, with an exponentially small sampling correction at finite flux. By contrast, for a straight-bond Peierls source, a low-frequency mass, and a fixed-envelope susceptibility, the viscosity--conductivity comparison exhibits an algebraic deviation, whose leading coefficient follows from a weak-field expansion.
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BibTeX
@misc{shu2026gaussianbond,
title = {{Gaussian-Bond Hall Viscosity and Nonlocal Hall Response of a Sampled Landau Level}},
author = {Danyu Shu and Ryotaro Sano and Ai Yamakage and Hiroshi Funaki and Mamoru Matsuo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.27059},
eprint = {2605.27059},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.27059},
}
RIS
TY - UNPB
TI - Gaussian-Bond Hall Viscosity and Nonlocal Hall Response of a Sampled Landau Level
AU - Danyu Shu
AU - Ryotaro Sano
AU - Ai Yamakage
AU - Hiroshi Funaki
AU - Mamoru Matsuo
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2605.27059
UR - https://arxiv.org/abs/2605.27059
AB - Hall viscosity on a lattice depends on how strain changes microscopic hopping amplitudes. For a specified Gaussian envelope, bond-length derivatives close on the undeformed hopping, expressing the stress as an embedded momentum Hessian and relating the viscosity to higher-order band geometry. In the Kapit--Mueller parent family at rational flux, we show that the stress response equals the strain curvature of the sampled-LLL Gram matrix. The density-normalized viscosity approaches the continuum value 1/4, with an exponentially small sampling correction at finite flux. By contrast, for a straight-bond Peierls source, a low-frequency mass, and a fixed-envelope susceptibility, the viscosity--conductivity comparison exhibits an algebraic deviation, whose leading coefficient follows from a weak-field expansion.
ER -