Representing Gutzwiller-Projected Variational Wavefunctions as Matrix Product States

Gapless free fermion states are notoriously challenging to represent with tensor network state methods. In a recent breakthrough, Fishman and White [PRB 92, 075132 (2015)] described an algorithm for efficiently representing the ground states of fermionic quadratic Hamiltonians in one spatial dimension as matrix product states (MPSs). We investigate generalizations of this method to construct efficient MPS representations of Gutzwiller-projected model variational wavefunctions for various quantum spin liquid states in 1D and quasi-1D. We benchmark our approach on a single half-filled band of spin-1/2 fermionic spinons---Gutzwiller projection of this state is known to be a quantitatively accurate description of the ground state of the 1D nearest-neighbor Heisenberg antiferromagnet. We then march toward 2D by considering quasi-1D incarnations of U(1) spin liquids on both the triangular and kagome lattices. We will compare the numerical effort of these calculations to that required for traditional variational Monte Carlo techniques, as well as comment on the feasibility of our approach for constructing good initial states for ground-state DMRG simulations of model Hamiltonians.