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We find a breakdown of the critical dynamic scaling in the coarseningdynamics of an antiferromagnetic {\em XY} model on the kagome lattice when thesystem is quenched from disordered states into the Kosterlitz-Thouless ({\emKT}) phases at low temperatures. There exist multiple growing length scales:the length scales of the average separation between fractional vortices arefound to be {\em not} proportional to the length scales of the quasi-ordereddomains. They are instead related through a nontrivial power-law relation. Thelength scale of the quasi-ordered domains (as determined from optimal collapseof the correlation functions for the order parameter $\exp[3 i \theta (r)]$)does not follow a simple power law growth but exhibits an anomalous growth withtime-dependent effective growth exponent. The breakdown of the critical dynamicscaling is accompanied by unusual relaxation dynamics in the decay offractional ($3\theta$) vortices, where the decay of the vortex numbers ischaracterized by an exponential function of logarithmic powers in time.

Coarsening Dynamics of an Antiferromagnetic XY model on the Kagome Lattice: Breakdown of the Critical Dynamic Scaling