Variational wavefunctions for topologically-ordered Fermi liquids

Quantum spin liquids provide a clear demonstration of topological order arising from magnetic frustration. These phases are most often studied in systems with localized spin-1/2 moments, where Gutzwiller-projected spinon wavefunctions can be effectively used to construct variational ansatzes for frustrated Heisenberg models. We generalize this procedure to allow for charge fluctuations - driven either through finite Hubbard repulsion or through doping - via the introduction of "ancilla" qubits, originally proposed in [Phys Rev R, 023172 (2020)]. We employ variational Monte Carlo techniques to calculate observables of these trial wavefunctions and optimize their energies against the two-dimensional Fermi-Hubbard model; in particular, we study the magnetic and charge correlations driven by the underlying spin liquid.