Next generation multi-scale quantum simulation software for strongly correlated materials

Abstract

Many technologically important materials display complex behavior due to strong electronic correlations. These include magnets, magnetoresistive materials, lanthanides and actinides and high temperature superconductors. Some of these materials display complex phase diagrams with multiple competing ground states, spin and charge ordering and complex excitations like those associated with spin and charge separation. An unbiased treatment of these phenomena requires a theory able to treat the correlations over all relevant length scales. In part, due to the minus sign problem, numerically exact methods employed to study these systems scale exponentially. Thus, despite great recent progress such as the development of the dynamical mean field approximation and its cluster extensions, there is as yet no unbiased study of these complex phenomena. The Multi-Scale Many-Body (MSMB) formalism and algorithms address these problems by separating the correlations into different length scales and treating each with an appropriate approximation: strong correlations at short length scales are treated by numerically exact Quantum Monte Carlo (QMC) simulations, those at intermediate length scales are treated by Feynman diagrammatic methods, while the weak correlations at long length scales are treated by a (dynamical) mean field approximation with a self-consistently determined effective medium.