Coherence properties of holes subject to a fluctuating spin chirality

The coherence properties of holes coupled to short-ranged chiral spin fluctuations with a characteristic chiral spin fluctuation time ${\mathrm{\tau }}_{\mathrm{ch}}$=${\mathrm{\omega }}_{\mathrm{ch}}^{\mathrm{-}1}$ are investigated in two dimensions. At temperatures kT≪4${\mathrm{\pi }}^2$〈${\mathrm{\phi }}^2$ ${\mathrm{〉}}^{\mathrm{-}1}$ħ${\mathrm{\omega }}_{\mathrm{ch}}$ hole quasiparticles exist and propagate with a renormalized mass ${\mathit{m}}^{\mathrm{*}}$/m=1+〈${\mathrm{\phi }}^2$〉ħ/16π${\mathit{ma}}_0^2$ ${\mathrm{\omega }}_{\mathrm{ch}}$. $langle phi sup 2 rangle— is the amplitude of the local fictitious flux fluctuation and ${\mathit{a}}_0$ is a lattice cutoff. At temperatures kT≫4${\mathrm{\pi }}^2$〈${\mathrm{\phi }}^2$ ${\mathrm{〉}}^{\mathrm{-}1}$ħ${\mathrm{\omega }}_{\mathrm{ch}}$ an effective-mass approximation is invalid and we find that the hole diffuses according to a logarithmic diffusion law in the quasistatic chiral field. The unusual diffusion law is a consequence of the long-ranged nature of the gauge field. The result shows that the holes do not form a coherent quantum fluid in the quasistatic regime.