# On the description of composite bosons in discrete models

## TL;DR

This paper critically examines the coboson ansatz for composite bosons, revealing its limitations in simple models and emphasizing the importance of dimensionality in many-body ground state behavior.

## Contribution

It investigates the validity of the coboson ansatz in simple models, highlighting the role of dimensionality and entanglement in many-body systems.

## Key findings

- Short-range interactions and high entanglement alone do not validate the ansatz.
- Dimensionality significantly influences the ground state behavior.
- The ansatz's applicability is limited in certain simple models.

## Abstract

The understanding of the behaviour of systems of identical composite bosons has progressed significantly in connection with the analysis of the entanglement between constituents and the development of coboson theory. The basis of these treatments is a coboson ansatz for the ground state of a system of N pairs, stating that in appropriate limits this state is well approximated by the account of Pauli exclusion in what would otherwise be the product state of N independent pairs, each described by the single-pair ground state. In this work we study the validity of this ansatz for particularly simple problems, and show that short-ranged attractive interactions in very dilute limits and a single-pair ground state with very large entanglement are not enough to render the ansatz valid. On the contrary, we find that the dimensionality of the problem plays a crucial role in the behaviour of the many-body ground state.