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Recently, quantum analogs of classical Gibbs samplers have been introduced—quantum Markov chains that generalize Glauber or Metropolis dynamics and serve as models of nature’s thermalization process. In this work, we show that every one-dimensional quantum Hamiltonian (spin chains) with short-range interactions admits a quantum Gibbs sampler with a system-size independent, optimal spectral gap at all finite temperatures. As a consequence, their Gibbs states can be prepared in polylogarithmic depth and exhibit exponential clustering of correlations, extending the classic result of Araki (1969). (Joint workÌýÌýwith Thiago Bergamaschi.)