  The interplay between spin and charge degrees of freedom arising from doping
a Mott insulating quantum spin liquid (QSL) has been a topic of research for
several decades. Calculating properties of these fractionalized metallic states
in single-band models are generally restricted to mean-field patron
descriptions and small fluctuations around these states, which are insufficient
for quantitative comparison of observables to measurements performed in
strongly-correlated systems. In this work, we numerically study a class of
correlated electronic wavefunctions which support fractionalized spin and
charge excitations and which fully take into account gauge fluctuations through
the enforcement of local Hilbert space constraints. By optimizing the energy of
these wavefunctions against the hole-doped Fermi Hubbard Hamiltonian, we obtain
a variational ansatz for describing the low-energy physics of this model. We
compare measurements of hole-induced spin-spin correlation functions to
measurements taken in low temperature cold-atom simulations of the Hubbard
model and find quantitative agreement between the two. In particular, we
demonstrate the emergence of magnetic polaron correlations in these metallic
states.
