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.
Categories: cond-mat.str-el