Fock-space recursive Green’s Function for many-fermion correlation functions

Many-fermion problems suffer from the exponential growth of Hilbert space with system size, resulting in prohibitive computational resource requirements for calculating spectrum or manyfermion correlation functions. Methods such as Lanczos and Density Matrix Renormalization Group (DMRG) allow the determination of extremal eigenvalues and eigenvectors in low dimensions. However, there are currently no alternatives for computing all elements of the many-fermion correlation function or the resolvent operator at arbitrary energy other than Exact diagonalization (ED) or direct inversion (DI). The spectrum of the resolvent operator can be used to study important problems such as many-body localization. It also allows calculating few-fermion Green's functions in interacting ground states. In this talk, we will look at a novel technique [1] that can serve as a memory-efficient alternative to ED or DI for computing the resolvent operator. Our approach reorganizes the Hilbert space into a structured lattice in the Fock space allowing the use of the well-known recursive Green's function method. We will demonstrate that in our technique, the memory requirement is suppressed by the system size than that needed for ED/DI on the same size lattice. This ‘Fock-space Recursive Green’s Function’ scheme does not rely on Hamiltonian symmetries, sparseness, or boundary conditions, unlike Lanczos or DMRG. As a demonstration, we will discuss the stability of fewhole bound states in an interacting ground state. We will briefly discuss applications for singleparticle spectral function, density-density correlation functions, and extension to spin ½ chains.