# Numerically exact approach to few-body problems far from a perturbative regime

## TL;DR

This paper introduces a numerically efficient, exact method for analyzing few-body quantum systems far from perturbative regimes, enabling accurate study of inter-particle correlations with limited computational resources.

## Contribution

It presents a novel basis construction method that surpasses traditional cut-off approaches, allowing exact calculations in complex many-body quantum systems.

## Key findings

- Effective basis construction enables exact calculations with limited resources.
- Studied quantum correlations in bosonic and fermionic systems in 1D traps.
- Method applicable far from perturbative regimes, capturing strong correlations.

## Abstract

Recent developments of experimental techniques in the field of ultra-cold gases open a path to study the crossover from 'few' to 'many' on the quantum level. In this case, accurate description of inter-particle correlations is very important since it is believed that they can be utilized by quantum engineers in quantum metrology, quantum thermometry, quantum heat engines, {\it etc}. Unfortunately, a theoretical description of these correlations is very challenging since they are far beyond any variational approaches. By contrast, the exact many-body description rapidly hits numerical limitations due to an exponential increase of the many-body Hilbert space. In this work, we brush up a very effective method of constructing a many-body basis which originates in the physical argumentation. We show that, in contrast to the commonly used approach of a straightforward cut-off, it enables one to perform exact calculations with very limited numerical resources. As examples, we study quantum correlations in systems of spinless bosons and two-component mixtures of fermions confined in a one-dimensional harmonic trap being far from the perturbative regime.