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

Abstract

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

arXiv comment5 pages + supplemental material