Real-space variational Gutzwiller wave functions for the Anderson-Hubbard model

TL;DR

This paper investigates the effectiveness of partially-projected Gutzwiller variational wavefunctions in modeling disordered interacting fermionic systems, identifying minimal parameter sets needed for accurate ground state descriptions across disorder regimes.

Contribution

It compares various variational states with exact solutions to determine the minimal parameters needed for accurate modeling of disordered systems.

Findings

Spatial charge density variations suffice for weak/intermediate disorder when screening is included.

In strong disorder, inhomogeneous variational parameters are necessary.

The study guides efficient variational modeling of disordered fermionic systems.

Abstract

Partially-projected Gutzwiller variational wavefunctions are used to describe the ground state of disordered interacting systems of fermions. We compare several different variational ground states with the exact ground state for disordered one-dimensional chains, with the goal of determining a minimal set of variational parameters required to accurately describe the spatially-inhomogeneous charge densities and spin correlations. We find that, for weak and intermediate disorder, it is sufficient to include spatial variations of the charge densities in the product state alone, provided that screening of the disorder potential is accounted for. For strong disorder, this prescription is insufficient and it is necessary to include spatially inhomogeneous variational parameters as well.