Models of classical fields coupled to itinerant fermions appear commonly in condensed matter. We present an efficient technique to sample these classical fields. Instead of expensive direct diagonalization, we use the Kernel Polynomial Method (KPM) to stochastically estimate electron states and relevant observables. Our extension of KPM significantly improves stochastic convergence by leveraging locality, e.g. spatial decay of 2-point correlations. A GPU/MPI implementation enables practical treatment of tens of thousands of lattice sites. To demonstrate the method, we study complex spin textures in the Kondo lattice model. We observe mesoscale chiral domain coarsening and Z2 vortex dynamics. Other emergent phenomena includes metastable skyrmions and a chiral stripe phase that arises due to instability of standard helical order.
Finally, we discuss a generic spin liquid state that may explain the experimentally observed resistivity minima in compounds with large local magnetic moments, e.g. the pyrochlore oxides Pr2Ir2O7, Nd2Ir2O7 under pressure, and RInCu4 (R=Gd, Dy, Ho, Er and Tm).