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

TL;DR

This paper introduces a novel Hilbert space reorganization that significantly reduces memory requirements for computing many-fermion resolvents, enabling more efficient simulations of large fermionic systems without relying on traditional symmetry or sparsity assumptions.

Contribution

The authors develop a new recursive scheme that suppresses exponential memory growth inversely with system size, improving resolvent calculations for many-fermion problems.

Findings

Memory requirement decreases inversely with system size.

Allows computations without relying on Hamiltonian symmetries.

Enables handling of long-range interactions efficiently.

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.