# Efficient construction of many-body Fock states having the lowest energies

## TL;DR

This paper introduces a fast, simple algorithm for constructing many-body Fock bases from low-energy states, significantly improving the accuracy of exact diagonalization calculations for quantum systems.

## Contribution

The authors present a novel algorithm that efficiently generates low-energy many-body Fock states, enhancing the accuracy of quantum many-body calculations.

## Key findings

- The algorithm is insensitive to single-particle energy distributions.
- It can be applied to bosonic and fermionic systems with arbitrary particle numbers.
- Exact calculations using the new basis outperform standard approaches.

## Abstract

To perform efficient many-body calculations in the framework of the exact diagonalization of the Hamiltonian one needs an appropriately tailored Fock basis built from the single-particle orbitals. The simplest way to compose the basis is to choose a finite set of single-particle wave functions and find all possible distributions of a given number of particles in these states. It is known, however, that this construction leads to very inaccurate results since it does not take into account different many-body states having the same energy on equal footing. Here we present a fast and surprisingly simple algorithm for generating the many-body Fock basis build from many-body Fock states having the lowest non-interacting energies. The algorithm is insensitive to details of the distribution of single-particle energies and it can be used for an arbitrary number of particles obeying bosonic or fermionic statistics. Moreover, it can be easily generalized to a larger number of components. Taking as a simple example the system of two ultra-cold bosons in an anharmonic trap, we show that exact calculations in the basis generated with the algorithm are substantially more accurate than calculations performed within the standard approach.