A Renormalization Approach to Simulations of Quantum Effects in Nanoscale Magnetic Systems

Simulation of the dynamics of nanoscale systems are usually restricted to a purely classical description, which becomes inadequate once technological minimization reaches scales on which quantum mechanical effects become relevant. In this paper we propose a multiscale approach to estimate quantum corrections to such classical descriptions. Quantum fluctuations in a quantum magnet are absorbed into thermal fluctuations by a locally varying renormalization of the corresponding classical magnet. To obtain these renormalization factors we match results of a quantum Monte Carlo simulation to classical Monte Carlo simulations. Using error robust optimization methods, such as simplex and genetic algorithms, we obtain an optimal set of renormalized couplings of the classical magnet which exhibits the same properties as the quantum magnet. A spatially varying renormalization takes into account the larger quantum fluctuations in the vicinity of surfaces and magnetic interfaces. We discuss applications of the algorithm to multiscale simulations of the dynamics of magnetic systems.