Efficient linear scaling mapping for permutation symmetric Fock spaces

TL;DR

This paper introduces a linear-scaling mapping method for permutation symmetric Fock spaces, significantly simplifying matrix element calculations and enabling efficient large-scale many-body quantum simulations.

Contribution

The authors develop a novel mapping technique that reduces computational complexity to linear scaling, facilitating more efficient calculations in permutation symmetric Fock spaces.

Findings

Mapping simplifies matrix element calculations.

Computational cost scales linearly with space size.

Implementation available as FockMap library.

Abstract

Numerically solving a second quantised many-body model in the permutation symmetric Fock space can be challenging for two reasons: (i) an increased complication in the calculations of the matrix elements of various operators, and (ii) a poor scaling of the cost of these calculations with the Fock space size. We present a method that solves both these problems. We find a mapping that can be used to simplify the calculations of the matrix elements. The mapping is directly generated so its computational cost scales only linearly with the space size and is negligible even for large enough sizes that approach the thermodynamic limit. A fortran implementation of the method as a library - FockMap - is provided along with a test program.