Exact Insulating and Conducting Ground States of a Periodic Anderson Model in Three Dimensions

We present a class of exact ground states of a three-dimensional periodic Anderson model at $3/4$ filling. Hopping and hybridization of $d$ and $f$ electrons extend over the unit cell of a general Bravais lattice. Employing novel composite operators combined with 55 matching conditions the Hamiltonian is cast into positive semidefinite form. A product wave function in position space allows one to identify stability regions of an insulating and a conducting ground state. The metallic phase is a non-Fermi liquid with one dispersing and one flat band.

Figure 1

Unit cell ($I$) of an orthorhombic lattice at an arbitrary site $\mathbf{i}$ showing the primitive vectors ${\mathbf{x}}_{\tau }$ and indices $n$ of the sites in $I$. Arrows depict some of the hopping and hybridization matrix elements ($J=t,V$) extending over $I$.

Figure 2

Ground-state energy of the localized state expressed in terms of $(E_g/N_{\Lambda }+U)/|t_1^d|$ as a function of next-nearest neighbor hopping of $d$ electrons, $|t_2^d/t_1^d|$, for different values of $f$ hopping $z=|t_1^f/t_1^d|$; here $|V_1/V_0|\gg 1/2$.

Figure 3

Surfaces in parameter space representing stability regions of the insulating ground state ($I_1$ for $|V_1/V_0|<1/2$, $I_2$ for $|V_1/V_0|\gg 1/2$) and the conducting ground state ($C$).