Efficient computation of matrix elements of generic Slater determinants

TL;DR

This paper introduces an extended L"owdin strategy for efficiently computing matrix elements of generic Slater determinants, applicable to any number of fermionic operators and handling singular overlap matrices.

Contribution

It presents a novel extension of the L"owdin method enabling the calculation of matrix elements for arbitrary Slater determinants, including cases with singular overlap matrices.

Findings

Method effectively computes matrix elements for arbitrary fermionic operators.

Handles singular overlap matrices without numerical issues.

Applicable to complex many-fermion systems.

Abstract

We present an extension of the L\"owdin strategy to find arbitrary matrix elements of generic Slater determinants. The new method applies to arbitrary number of fermionic operators, even in the case of a singular overlap matrix.