Plaquette operators used in the rigorous study of ground-states of the Periodic Anderson Model in $D = 2$ dimensions

TL;DR

This paper introduces a novel method using plaquette operators to derive exact ground-states of the 2D periodic Anderson model, revealing a new localized phase and insights into metal-insulator transitions without requiring next-nearest neighbor interactions.

Contribution

It presents the first exact ground-states for the 2D periodic Anderson model with finite interaction, using a new type of plaquette operator that does not need extended Hamiltonian terms.

Findings

Introduction of a new localized phase in 2D PAM

Exact ground-states obtained without next-nearest neighbor terms

Localization loss linked to density-density correlation breakdown

Abstract

The derivation procedure of exact ground-states for the periodic Anderson model (PAM) in restricted regions of the parameter space and D=2 dimensions using plaquette operators is presented in detail. Using this procedure, we are reporting for the first time exact ground-states for PAM in 2D and finite value of the interaction, whose presence do not require the next to nearest neighbor extension terms in the Hamiltonian. In order to do this, a completely new type of plaquette operator is introduced for PAM, based on which a new localized phase is deduced whose physical properties are analyzed in detail. The obtained results provide exact theoretical data which can be used for the understanding of system properties leading to metal-insulator transitions, strongly debated in recent publications in the frame of PAM. In the described case, the lost of the localization character is connected to the break-down of the long-range density-density correlations rather than Kondo physics.