  Presenting exact solutions for the two dimensional periodic Anderson model
with finite and nonzero on-site interaction U>0, we are describing a rigorous
non-Fermi liquid phase in normal phase and 2D. This new state emerges in
multi-band interacting Fermi systems above half filling, being generated by a
flat band effect. The momentum distribution function n_k together with its
derivatives of any order is continuous. The state possesses a well defined
Fermi energy, but the Fermi momentum concept is not definable, so the Fermi
surface in k-space is missing. The state emerges in the vicinity of a Mott
insulating phase when lattice distortions are present, is highly degenerated
and paramagnetic. A gap is present at high U in the density of low lying
excitations. During low lying excitations, quasi-particles are not created
above the Fermi level, only the number of particles at the Fermi energy
increases.
