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.

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.