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 $C(t) \equiv \langle \sigma^-_x(t) \sigma^+_x(0)\rangle$ 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.

Statistical Mechanics (cond-mat.stat-mech); Quantum Physics (quant-ph)

arXiv:2610.20724 [cond-mat.stat-mech]

(or arXiv:2610.20724v1 [cond-mat.stat-mech] for this version)

https://doi.org/10.48550/arXiv.2610.20724 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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