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 $O(\log N+\log(1/\epsilon))$. 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.

arXiv:2610.28600 [quant-ph]

(or arXiv:2610.28600v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.28600 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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