Exact Self-Consistent Effective Hamiltonian Theory

Exact solutions to interacting many-body fermionic systems, especially in dimensions higher than one, have always been the holy grail for quantum physicists. Computationally, the exponential growth of the Fock-Hilbert space's dimension with the size of the system (number of fermions, for example) also makes it a benchmark problem for quantum computations. We propose a general variational fermionic many-body wavefunction that generates an effective Hamiltonian in a quadratic form, which can then be exactly solved. The theory can be constructed within the density functional theory framework, and a self-consistent scheme is proposed for solving the exact density functional theory. Numerical algorithm based on the theory and results on some prototype systems are presented to illustrate the potential of the theory.