CONAN -- the cruncher of local exchange coefficients for strongly interacting confined systems in one dimension

TL;DR

This paper introduces CONAN, an open-source algorithm and software for efficiently computing exchange coefficients in strongly interacting one-dimensional particle systems, applicable to various external potentials.

Contribution

The paper presents a novel algorithm and software tool, CONAN, for calculating exchange coefficients in 1D strongly interacting systems with arbitrary traps, scalable to about 35 particles.

Findings

CONAN reliably computes exchange coefficients for systems up to 35 particles.

Computation time scales approximately as N^{3.5} for system size N.

The software performs calculations within seconds for N=10 and minutes for N=20.

Abstract

We consider a one-dimensional system of particles with strong zero-range interactions. This system can be mapped onto a spin chain of the Heisenberg type with exchange coefficients that depend on the external trap. In this paper, we present an algorithm that can be used to compute these exchange coefficients. We introduce an open source code CONAN (Coefficients of One-dimensional N-Atom Networks) which is based on this algorithm. CONAN works with arbitrary external potentials and we have tested its reliability for system sizes up to around 35 particles. As illustrative examples, we consider a harmonic trap and a box trap with a superimposed asymmetric tilted potential. For these examples, the computation time typically scales with the number of particles as $O(N^{3.5 \pm 0.4})$. Computation times are around 10 seconds for $N=10$ particles and less than 10 minutes for $N=20$ particles.