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Similarity transformation of the Hubbard Hamiltonian using a Gutzwillercorrelator leads to a non-Hermitian effective Hamiltonian, which can beexpressed exactly in momentum-space representation, and contains three-bodyinteractions. We apply this methodology to study the two-dimensional Hubbardmodel with repulsive interactions near half-filling in the intermediateinteraction strength regime ($U/t=4$). We show that at optimal or near optimalstrength of the Gutzwiller correlator, the similarity transformed Hamiltonianhas extremely compact right eigenvectors, which can be sampled to high accuracyusing the Full Configuration Interaction Quantum Monte Carlo (FCIQMC) method,and its initiator approximation. Near-optimal correlators can be obtained usinga simple projective equation, thus obviating the need for a numericaloptimisation of the correlator. The FCIQMC method, as a projective technique,is well-suited for such non-Hermitian problems, and its stochastic nature canhandle the 3-body interactions exactly without undue increase in computationalcost. The highly compact nature of the right eigenvectors means that theinitiator approximation in FCIQMC is not severe, and that large lattices can besimulated, well beyond the reach of the method applied to the original HubbardHamiltonian. Results are provided in lattice sizes upto 50 sites and comparedto auxiliary-field QMC. New benchmark results are provided in the offhalf-filling regime, with no severe sign-problem being encountered. Inaddition, we show that methodology can be used to calculate excited states ofthe Hubbard model and lay the groundwork for the calculation of observablesother than the energy.

Compact numerical solutions to the two-dimensional repulsive Hubbard model obtained via non-unitary similarity transformations