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Complete Modified Logarithmic Sobolev Inequalities for one-dimensional quantum Spin Chain
Abstract
We prove a complete modified logarithmic Sobolev inequality with a system-size-independent constant for Chen--Kastoryano--Gilyén Gibbs samplers on one-dimensional spin chain at every fixed positive temperature. The result holds for Hamiltonians with bounded finite-range interactions, including noncommuting and spatially nonuniform interactions. It yields trace and diamond mixing times of order O(log N+log(1/ε)). The proof establishes complete spatial entropy factorization and absorbs quasi-local errors as conditional relative entropy at the original joint state and reference. The static estimate also yields a system-size-independent CMLSI for the single-site Petz heat-bath and regularised heat-bath dynamics.
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BibTeX
@misc{gao2026complete,
title = {{Complete Modified Logarithmic Sobolev Inequalities for one-dimensional quantum Spin Chain}},
author = {Li Gao and Jingyu Guo and Sihao Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28600},
eprint = {2610.28600},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28600},
}
RIS
TY - UNPB
TI - Complete Modified Logarithmic Sobolev Inequalities for one-dimensional quantum Spin Chain
AU - Li Gao
AU - Jingyu Guo
AU - Sihao Wang
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.28600
UR - https://arxiv.org/abs/2610.28600
AB - We prove a complete modified logarithmic Sobolev inequality with a system-size-independent constant for Chen--Kastoryano--Gilyén Gibbs samplers on one-dimensional spin chain at every fixed positive temperature. The result holds for Hamiltonians with bounded finite-range interactions, including noncommuting and spatially nonuniform interactions. It yields trace and diamond mixing times of order O(log N+log(1/ε)). The proof establishes complete spatial entropy factorization and absorbs quasi-local errors as conditional relative entropy at the original joint state and reference. The static estimate also yields a system-size-independent CMLSI for the single-site Petz heat-bath and regularised heat-bath dynamics.
ER -