Factorization in large-scale many-body calculations

TL;DR

This paper discusses a factorization approach to reduce storage requirements in large-scale many-body quantum calculations, specifically in configuration-interaction methods for fermion systems, leveraging symmetry properties.

Contribution

It introduces an exact factorization algorithm that significantly decreases storage needs in configuration-interaction calculations, applicable to systems with symmetry such as rotational invariance.

Findings

Reduces storage requirements by an order of magnitude or more.

Applicable to large-scale many-fermion systems with symmetry.

Implemented in the BIGSTICK code for serial and parallel computing.

Abstract

One approach for solving interacting many-fermion systems is the configuration-interaction method, also sometimes called the interacting shell model, where one finds eigenvalues of the Hamiltonian in a many-body basis of Slater determinants (antisymmeterized products of single-particle wavefunctions). The resulting Hamiltonian matrix is typically very sparse, but for large systems the nonzero matrix elements can nonetheless require terabytes or more of storage. An alternate algorithm, applicable to a broad class of systems with symmetry, in our case rotational invariance, is to exactly factorize both the basis and the interaction using additive/multiplicative quantum numbers; such an algorithm can reduce the storage requirements by an order of magnitude or more. We discuss factorization in general as well as in the context of a specific configuration-interaction code, BIGSTICK, which runs both on serial and parallel machines.