Tests of the Envelope Theory in One Dimension

TL;DR

This paper evaluates the envelope theory's effectiveness in approximating ground states of one-dimensional many-body systems with pairwise interactions, demonstrating its reliability across different models and particle types.

Contribution

It provides the first systematic testing of the envelope theory in one-dimensional systems with pairwise forces, including fermionic and bosonic models.

Findings

Envelope theory yields good bounds for ground state energies.

Accuracy depends on model parameters.

Effective for both fermionic and bosonic systems.

Abstract

The envelope theory is a simple technique to obtain approximate, but reliable, solutions of many-body systems with identical particles. The accuracy of this method is tested here for two systems in one dimension with pairwise forces. The first one is the fermionic ground state of the analytical Calogero model with linear forces supplemented by inverse-cube forces. The second one is the ground state of up to 100 bosons interacting via a Gaussian potential. Good bounds can be obtained depending on values of the model parameters.