Constructive fermionic matrix product states for projected Fermi sea

Projected wave functions offer a means of incorporating local correlation effects in gapless electronic phases of matter, like metals. Although such wave functions can be readily specified formally, computing their associated physical observables is challenging. Tensor network approaches offer a modern numerical method for this task. In this paper, we develop and demonstrate a constructive tensor-network approach for obtaining physical quantities, like fermion two-point functions and density-density correlation functions, for one-dimensional projected Fermi sea states. We benchmark our method against exact analytical results for spin-1/2 electrons subjected to the Gutzwiller projection, and then present results on spinless fermions with nearest-neighbor repulsion. For a state with two pairs of Fermi points, we reveal a correlation-dependent tuning of the characteristic wave vector of the charge density modulation in the system.