Lie algebraic similarity transformed Hamiltonians for lattice model systems

Abstract

We present a class of Lie algebraic similarity transformations generated by exponentials of two-body on-site Hermitian operators whose Hausdorff series can be summed exactly without truncation. The correlators are defined over the entire lattice and include the Gutzwiller factor ${n}_{i\ensuremath{\uparrow}}{n}_{i\ensuremath{\downarrow}}$, and two-site products of density $({n}_{i\ensuremath{\uparrow}}+{n}_{i\ensuremath{\downarrow}})$ and spin $({n}_{i\ensuremath{\uparrow}}\ensuremath{-}{n}_{i\ensuremath{\downarrow}})$ operators. The resulting non-Hermitian many-body Hamiltonian can be solved in a biorthogonal mean-field approach with polynomial computational cost. The proposed similarity transformation generates locally weighted orbital transformations of the reference determinant. Although the energy of the model is unbound, projective equations in the spirit of coupled cluster theory lead to well-defined solutions. The theory is tested on the one- and two-dimensional repulsive Hubbard model where it yields accurate results for small and medium sized interaction strengths.