Self-Consistent Effective Hamiltonian and its solution for the Hubbard Dimer and DImer Lattice*

We propose a general variational fermionic many-body wavefunction that generates two quadratic chiral-symmetry broken  effective Hamiltonians, each of which can then be solved exactly. 

We apply the theory to the  Hubbard dimers, and the corresponding lattice model and in the case of Hubbard Dimer, show that the exact eigenstate can be obtained by a linear combination of two chiral-symmetry broken states, each being the ground state of two quadratic effective Hamiltonian. The single-fermion excitation spectra show a persistent charge excitation gap due to the fermion-entanglement-induced pairing condensate. In addition, there is a pseudo-Majorana excitation band close to zero energy.