Dyson Field: A Quasiparticle Mapping for Multi-State Density Functional Theory

Yangyi Lu, Jiali Gao

Published Apr 20, 2026• 0 citations

Abstract

Multistate density functional theory (MSDFT) provides a rigorous variational framework for the simultaneous description of multiple electronic states through a matrix density, but practical implementations have relied on multiconfigurational many-body wavefunctions. Here, we introduce the Dyson field, ψ(r), an L×N matrix-valued function of the coordinate r that factorizes the matrix density as D(r) = ψ†(r)ψ(r). The elements of ψ(r) = {ψpA(r)} are shown to be Dyson orbitals connecting the n-electron states of interest to (n − 1)-electron ionization channels of size L, providing a direct physical interpretation of the matrix density in terms of electron removal amplitudes. Variational minimization of the MSDFT subspace energy with respect to the Dyson field yields a matrix Fock equation, in which the kinetic and external potential operators act locally, while Hartree and exchange–correlation effects appear as N×N matrix potentials, VH[D](r) and Vxc[D](r), that couple electronic states within the subspace. This formulation defines a quasiparticle reference system for MSDFT that is analogous to the Kohn–Sham orbitals in Hohenberg-Kohn DFT. In appropriate limits, the formalism reduces exactly to Kohn-Sham DFT for N = 1 and to the Tamm-Dancoff approximation of time-dependent DFT within the single-excitation manifold. More generally, the Dyson-field construction transforms MSDFT from a formally exact but wavefunction-dependent framework into an orbital-based theory, opening a practical route to self-consistent, density-based treatments of strongly correlated and electronically coupled states.

DOI: 10.65215/ltspreprints.2026.04.20.000192

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