Memory efficient Fock-space recursion scheme for computing many-fermion resolvents

Abstract

A fundamental roadblock to the exact numerical solution of many-fermion problems is the exponential growth of the Hilbert space with system size. It manifests as extreme dynamical memory and computation-time requirements for simulating many-fermion processes. Here we construct a novel reorganization of the Hilbert space to establish that the exponential growth of dynamical-memory requirement is suppressed inversely with system size in our approach. Consequently, the state-of-the-art resolvent computation can be performed with substantially less memory. The memory-efficiency does not rely on Hamiltonian symmetries, sparseness, or boundary conditions and requires no additional memory to handle long-range density-density interaction and hopping. We provide examples calculations of interacting fermion ground state energy, the many-fermion density of states and few-body excitations in interacting ground states in one and two dimensions.