  We study a set of many-body wave-functions of Fermions that are naturally
written using momentum space basis and allow for quantum superposition of
Fermion occupancy, $\{n_{\bf k}\}$. This {enables} us to capture the
fluctuations of the Fermi-surface {(FS)} -- the singularly most important
signature of a metal. We bench-mark our results in one spatial dimensions (1D)
to show that these wave-functions allow for quantitative understanding of the
Tomonaga-Luttinger liquid (TLL); computations of certain correlators using them
can in fact be extended to larger systems sizes compared to conventional exact
diagonalization (ED) allowing for a more systematic comparison with
bosonization techniques. Finally we show that this basis may be useful for
obtaining fixed-point wave-function for strongly correlated metals {in
dimensions greater that one}. In particular, we study the case of coherent
(equal) superposition of elliptical FS {in continuum (2D) and on a} square
lattice{. In case of the former, our variational wave-function systematically
interpolates between the phenomenology of the Fermi liquid ground state, i.e.,
finite single-Fermion residue at a sharp FS, to a non-Fermi liquid (NFL) with
zero residue. In the NFL the jump in $\langle n_{\bf k}\rangle$ at the FS is
replaced by a point of inflection (similar to a 1D TLL) whose contour is
consistent with the Luttinger Theorem. In case of the square lattice, we} find
highly anisotropic distribution of the quasi-particle residue, which, at finite
resolution has an uncanny resemblance to the Fermi-arcs{, albeit at zero
temperature,} seen in the pseudo-gap state of the cuprates.
