For 1D quantum spin chains with commuting Hamiltonians, positivity of the modified logarithmic Sobolev constant for heat-bath dynamics follows from an exponential clustering condition and a strong quasi-factorization of relative entropy.
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On the modified logarithmic Sobolev inequality for the heat-bath dynamics for 1D systems
For 1D quantum spin chains with commuting Hamiltonians, positivity of the modified logarithmic Sobolev constant for heat-bath dynamics follows from an exponential clustering condition and a strong quasi-factorization of relative entropy.