# Bound cyclic systems with the envelope theory

## TL;DR

This paper adapts the envelope theory, a method for approximating quantum systems, to cyclic systems where particles interact only with their immediate neighbors, enabling easier computation of such systems.

## Contribution

The paper extends the envelope theory to cyclic systems with local interactions, providing a new approach for approximate solutions of these quantum configurations.

## Key findings

- Enables approximate solutions for cyclic quantum systems.
- Applicable to systems with arbitrary kinematics and potentials.
- Simplifies computation of complex many-body interactions.

## Abstract

Approximate but reliable solutions of a quantum system with $N$ identical particles can be easily computed with the envelope theory, also known as the auxiliary field method. This technique has been developed for Hamiltonians with arbitrary kinematics and one- or two-body potentials. It is adapted here for cyclic systems with $N$ identical particles, that is to say systems in which a particle $i$ has only an interaction with particles $i-1$ and $i+1$ (with $N+1\equiv 1$).