  We present an exact ground state solution of a quantum dimer model introduced
in Ref.[1], which features ordinary bosonic spin-singlet dimers as well as
fermionic dimers that can be viewed as bound states of spinons and holons in a
hole-doped resonating valence bond liquid. Interestingly, this model captures
several essential properties of the metallic pseudogap phase in high-$T_c$
cuprate superconductors. We identify a line in parameter space where the exact
ground state wave functions can be constructed at an arbitrary density of
fermionic dimers. At this exactly solvable line the ground state has a huge
degeneracy, which can be interpreted as a flat band of fermionic excitations.
Perturbing around the exactly solvable line, this degeneracy is lifted and the
ground state is a fractionalized Fermi liquid with a small pocket Fermi surface
in the low doping limit.
