  Similarity transformation of the Hubbard Hamiltonian using a Gutzwiller
correlator leads to a non-Hermitian effective Hamiltonian, which can be
expressed exactly in momentum-space representation, and contains three-body
interactions. We apply this methodology to study the two-dimensional Hubbard
model with repulsive interactions near half-filling in the intermediate
interaction strength regime ($U/t=4$). We show that at optimal or near optimal
strength of the Gutzwiller correlator, the similarity transformed Hamiltonian
has extremely compact right eigenvectors, which can be sampled to high accuracy
using the Full Configuration Interaction Quantum Monte Carlo (FCIQMC) method,
and its initiator approximation. Near-optimal correlators can be obtained using
a simple projective equation, thus obviating the need for a numerical
optimisation of the correlator. The FCIQMC method, as a projective technique,
is well-suited for such non-Hermitian problems, and its stochastic nature can
handle the 3-body interactions exactly without undue increase in computational
cost. The highly compact nature of the right eigenvectors means that the
initiator approximation in FCIQMC is not severe, and that large lattices can be
simulated, well beyond the reach of the method applied to the original Hubbard
Hamiltonian. Results are provided in lattice sizes upto 50 sites and compared
to auxiliary-field QMC. New benchmark results are provided in the off
half-filling regime, with no severe sign-problem being encountered. In
addition, we show that methodology can be used to calculate excited states of
the Hubbard model and lay the groundwork for the calculation of observables
other than the energy.

Strongly Correlated Electrons;Computational Physics