Global fermionic mode optimization via swap gates

We propose a general approach to find an optimal representation of a quantum many body wave function for a given error margin via global fermionic mode optimization. The stationary point on a fixed rank matrix product state manifold is obtained via a joint optimization on the Grassman manifold [Phys. Rev. Lett. 117, 210402] together with swap gates controlled permutations. The minimization of the global quantity, the block entropy area, guarantees that the method fulfills all criteria with respect to partial derivatives. Numerical results via large scale density matrix renormalization group simulations on strongly correlated molecular systems and two-dimensional fermionic lattice models are discussed.