Subexponential Decay of Local Correlations from Diffusion-Limited Dephasing

Chaotic quantum systems at finite entropy density are expected to act as their own heat baths, rapidly dephasing local quantum superpositions. We argue that in fact this dephasing is generically subexponential in one-dimensional systems with conservation laws: all local correlation functions decay as exp[-O(t^{α})] with 0≤α≤2/3, even when the operators are orthogonal to all hydrodynamic modes. The mechanism is diffusion-limited dephasing, in which rare low-entropy regions ("voids") protect quantum coherences. This intrinsically quantum effect lies beyond standard hydrodynamics and disappears under extrinsic dephasing. In random charge-conserving circuits we find α=1/2, while in generic translation-invariant Floquet systems we bound α≤2/3. Our arguments are general, subject principally to the assumption that thermal fluctuations can create regions of zero entropy density. In systems with energy conservation, this assumption is automatically satisfied because of the third law of thermodynamics.