Systematic construction of density functionals based on matrix product state computations

2016/03/31 by Michael Lubasch, Johanna I Fuks, Johanna I. Fuks +5 · 20 citations
Chemistry · Materials Science · Physics and Astronomy · #Advanced Physical and Chemical Molecular Interactions #Ansatz #Computation #Density matrix #Fermion #Lattice (music) #Machine Learning in Materials Science #Matrix product state #Product (mathematics) #Quantum many-body systems #cond-mat.str-el

paper · pdf · doi:10.1088/1367-2630/18/8/083039

published in New Journal of Physics 18(8), 083039 (IOP Publishing) · 16 pages, 6 figures, accepted version

openalex publication_date 2016/08/19 · arxiv created 2016/08/25 · arxiv updated 2016/08/29 · openalex created_date 2016/09/16 · openalex updated_date 2026/08/05

Abstract

We propose a systematic procedure for the approximation of density functionals in density functional theory that consists of two parts. First, for the efficient approximation of a general density functional, we introduce an efficient ansatz whose non-locality can be increased systematically. Second, we present a fitting strategy that is based on systematically increasing a reasonably chosen set of training densities. We investigate our procedure in the context of strongly correlated fermions on a one-dimensional lattice in which we compute accurate training densities with the help of matrix product states. Focusing on the exchange-correlation energy, we demonstrate how an efficient approximation can be found that includes and systematically improves beyond the local density approximation. Importantly, this systematic improvement is shown for target densities that are quite different from the training densities.

Citations

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