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Variational Diagrammatic Monte Carlo To Solve the Electronic Structure Problem
Speaker: Kristjan Haule (Rutgers University)
Due to recent advances in Monte Carlo summation of high-order Feynman diagrams many previously unsolvable problems became numerically exactly solvable. Examples are the solution of a generic quantum impurity problem and the solution of the unitary fermi gas, which were solved by the continuous time quantum Monte Carlo and the bold diagrammatic Monte Carlo methods, respectively. However, numerically controllable solution of the realistic solid state problem with the long-range Coulomb repulsion remained a challenge until recently. In Ref.[1] we developed the Variational Diagrammatic Monte Carlo (VDMC) method, which sums up all Feynman diagrams up to high orders and uses ideas from variational perturbation theory to speed up the convergence of the series, giving numerically exact solution in classical model of solids, the uniform electron gas at metallic densities. While most of the previous Monte Carlo methods suffer from the so-called sign problem, VDMC organizes Feynman diagrams so that it combines factorially large number of diagrams together, consequently massively reducing the fermionic sign problem and achieving so-called 'sign-blessing', where the series expansion converges. This method allowed us to calculate the momentum and frequency resolved spin and charge response functions with the unprecedented accuracy, beating the established diffusion Monte Carlo results. Its efficiency is comparable to the famous GW method, which is extensively used as ab-initio tool, hence the implementation of VDMC in realistic settings is within reach, and can pave the way for controlled simulations of electronic structure from first principle in moderately correlated solids in not too distant future.
[1] Feynman's solution of the quintessential problem in solid state physics, Kun Chen and Kristjan Haule, arXiv:1809.04651.
Host: David Vanderbilt