Dissipative spin dynamics in hot quantum paramagnets

TL;DR

This paper employs a functional renormalization approach to analyze spin dynamics in hot quantum paramagnets, revealing diffusive behavior in higher dimensions and superdiffusion in lower dimensions, with implications for understanding high-temperature spin correlations.

Contribution

It introduces a non-perturbative method to compute the dynamic structure factor and spin diffusion in quantum Heisenberg magnets across different dimensions, extending beyond hydrodynamic limits.

Findings

In three dimensions, the spin diffusion coefficient is about 30% larger than experimental values.

In two dimensions, the spin diffusion coefficient diverges logarithmically with frequency.

In one dimension, the results agree with the dynamical exponent z=3/2 from integrable spin chain theories.

Abstract

We use the functional renormalization approach for quantum spin systems developed by Krieg and Kopietz [Phys. Rev. B $\mathbf{99}$, 060403(R) (2019)] to calculate the spin-spin correlation function $G (\boldsymbol{k}, \omega )$ of quantum Heisenberg magnets at infinite temperature. For small wavevectors $\boldsymbol{k} $ and frequencies $\omega$ we find that $G ( \boldsymbol{k}, \omega )$ assumes in dimensions $d > 2$ the diffusive form predicted by hydrodynamics. In three dimensions our result for the spin-diffusion coefficient ${\cal{D}}$ is somewhat smaller than previous theoretical predictions based on the extrapolation of the short-time expansion, but is still about $30 \%$ larger than the measured high-temperature value of ${\cal{D}}$ in the Heisenberg ferromagnet Rb$_2$CuBr$_4\cdot$2H$_2$O. In reduced dimensions $d \leq 2$ we find superdiffusion characterized by a frequency-dependent complex spin-diffusion coefficient ${\cal{D}} ( \omega )$ which diverges logarithmically in $d=2$, and as a power-law ${\cal{D}} ( \omega ) \propto \omega^{-1/3}$ in $d=1$. Our result in one dimension implies scaling with dynamical exponent $z =3/2$, in agreement with recent calculations for integrable spin chains. Our approach is not restricted to the hydrodynamic regime and allows us to calculate the dynamic structure factor $S ( \boldsymbol{k} , \omega )$ for all wavevectors. We show how the short-wavelength behavior of $S ( \boldsymbol{k}, \omega )$ at high temperatures reflects the relative sign and strength of competing exchange interactions.