Fundamental building blocks of strongly correlated wave functions

TL;DR

This paper introduces a new algebraic structure for many-fermion wave functions, representing them with a finite set of antisymmetric shapes, which advances the understanding of strongly correlated electron systems.

Contribution

It presents a novel algebraic framework that expresses many-fermion wave functions in terms of a finite number of shapes, generalizing the Slater determinant concept to higher dimensions.

Findings

Number of shapes is exactly $N!^{d-1}$ in $d$ dimensions.

An improved algorithm for generating all fermion shapes in odd-dimensional spaces.

Contextualization within current research on strongly correlated electrons.

Abstract

The calculation of realistic N-body wave functions for identical fermions is still an open problem in physics, chemistry, and materials science, even for N as small as two. A recently discovered fundamental algebraic structure of many-body Hilbert space allows an arbitrary many-fermion wave function to be written in terms of a finite number of antisymmetric functions called shapes. Shapes naturally generalize the single-Slater-determinant form for the ground state to more than one dimension. Their number is exactly $N!^{d-1}$ in $d$ dimensions. An efficient algorithm is described to generate all fermion shapes in spaces of odd dimension, which improves on a recently published general algorithm. The results are placed in the context of contemporary investigations of strongly correlated electrons.