• Bose-Hubbard model
• entanglement entropy
• quantum phase transitions

We examine some aspects of the quantum entanglement in a system composed of N impenetrable boson particles moving on a 1D optical lattice and confined by a harmonic trap.
We introduce the Bose-Hubbard model, which defines our theoretical framework, and we describe the quantum phase transitions in this model. We also introduce the concept of entanglement entropy, and we examine the scaling behaviour of the entropy depending on the lattice-size L and the trap-size l.
Our results concern the numerical evaluation of the entanglement entropy of the system:
We compute the half-lattice entropy and the one-particle entropy in the limits of infinite lattice-size and infinite trap-size, then we examine their dependence on the number of particles N, focusing on their asymptotic behaviour for large values of N.