Momentum-dependent local ansatz approach to correlated electrons

TL;DR

This paper reviews the momentum-dependent local ansatz (MLA) wavefunction approach for accurately describing correlated electron states in solids across various interaction regimes, including strongly correlated systems, by introducing a hybrid wavefunction.

Contribution

It introduces the MLA-HB wavefunction that overcomes limitations of previous wavefunctions, improving the description of electron correlations from weak to strong interactions.

Findings

MLA accurately describes correlated electrons from weak to intermediate Coulomb interactions.

MLA-HB improves the description in strongly correlated regimes.

Quasiparticle weight curve matches numerical renormalization group results.

Abstract

The wavefunction method provides us with a useful tool to describe electron correlations in solids at the ground state. In this paper we review the recent development of the momentum-dependent local ansatz wavefunction (MLA). It is constructed by taking into account two-particle excited states projected onto the local orbitals, and the momentum-dependent amplitudes of these states are chosen as variational parameters. The MLA describes accurately correlated electron states from the weak to the intermediate Coulomb interaction regime in infinite dimensions, and works well even in the strongly correlated region by introducing a new starting wavefunction called the hybrid (HB) wavefunction. The MLA-HB is therefore shown to overcome the limitation of the original local ansatz (LA) wavefunction as well as the Gutzwiller wavefunction. In particular, the calculated quasiparticle weight vs Coulomb interaction curve is shown to be close to that obtained by the numerical renormalization group approach. It is also shown that the MLA is applicable to the first-principles Hamiltonian.