# Exact results for the entanglement in 1D Hubbard models with spatial constraints

## TL;DR

This paper derives exact analytical formulas for bipartite entanglement entropy in 1D Hubbard models with spatial constraints, revealing how entanglement scales and can be controlled by interaction range and filling.

## Contribution

It provides the first exact formulas for entanglement in constrained 1D Hubbard models, elucidating the effects of spatial constraints on entanglement scaling and control.

## Key findings

- Entropy diverges logarithmically at thermodynamic limit except at half-filling
- Universal prefactor of 1/2 for entropy due to partial permutational invariance
- Entanglement can be maximized by tuning interaction range and filling

## Abstract

We investigate the entanglement in Hubbard models of hardcore bosons in $1D$, with an additional hardcore interaction on nearest neighbouring sites. We derive analytical formulas for the bipartite entanglement entropy for any number of particles and system size, whose ratio determines the system filling. At the thermodynamic limit the entropy diverges logarithmically for all fillings, except for half-filling, with the universal prefactor $1/2$ due to partial permutational invariance. We show how maximal entanglement can be achieved by controlling the interaction range between the particles and the filling which determines the empty space in the system. Our results show how entangled quantum phases can be created and controlled, by imposing spatial constraints on states formed in many-body systems of strongly interacting particles.