Recursive relations and quantum eigensolver algorithms within modified Schrieffer-Wolff transformations for the Hubbard dimer

We derive recursive relations for the Schrieffer--Wolff (SW) transformation applied to half-filled Hubbard dimer. While standard SW is set block-diagonalize transformed Hamiltonian solely at first order of perturbation, we infer from two types modifications, variational or iterative, that approach, even enforce homogeneous case, desired block-diagonalization infinite perturbation. The modified unitary transformations are then used design an test quantum algorithms adapted noisy and fault-tolerant era. This work paves way toward alternative general Hamiltonian.