Large-scale simulations of spin-density-wave order in frustrated lattices

We investigate spin-density-wave (SDW) phases within a generalized mean-field approximation. This approach incorporates the thermal fluctuations of SDW order and the development of short-range order above magnetic ordering temperatures $T_c$. Using a new Langevin dynamics method, we study mesoscale structures associated with triple-$\mathbf Q$ SDW states that are induced by Fermi surface nesting in triangular and kagome lattice Hubbard models. The core of our linear-scaling Langevin dynamics simulations is an efficient stochastic kernel polynomial method for computing the electron density matrix. We also investigate exotic phases above $T_c$ arising from preformed magnetic moments.