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 $C(t)\equiv ⟨{\sigma }_x^{-}(t){\sigma }_x^{+}(0)⟩$ can decay at most algebraically: $C(t)\gtrsim 1\mathrm{/}{t}^2$. This bound is not tight: in the large-anisotropy limit of the XXZ spin chain, at infinite temperature, we explicitly compute $C(t)\sim \sqrt{3}\mathrm{/}(18\sqrt{t})$. We also compute this decay rate in the XXZ spin chain for general easy-axis anisotropy, and estimate it to scale as $C(t)\sim t^{-2\mathrm{/}z}$ (for transport exponent $z$) in the chaotic models.