Long-lived local coherences at high temperature from frozen domain walls

Local coherences between distinct charge sectors--measured by the single-particle Green's function or the transverse spin autocorrelation function--do not overlap with hydrodynamic modes. At finite temperature, therefore, they decay faster than any power law in generic chaotic systems. We present a mechanism by which these coherences can persist anomalously long, for integrable and chaotic spin chains (including the XXZ and Fredkin spin chains) that obey a quantum group symmetry. We show--using a Mazur bound derived from the quantum-group symmetry, together with locality and a "non-undershoot" assumption--that the transverse spin autocorrelation function C(t) σ-x(t) σ+ x(0) can decay at most algebraically: C(t) 1/t squared. This bound is not tight: in the large-anisotropy limit of the XXZ spin chain, at infinite temperature, we explicitly compute C(t) about sqrt 3 /(18 sqrt t). We also compute this decay rate in the XXZ spin chain for general easy-axis anisotropy, and estimate it to scale as C(t) about t-2/z (for transport exponent z) in the chaotic models.