Entanglement entropy in a spin-boson model and level crossings in an Ising dimer with Dzyaloshinskii-Moriya interaction

We calculate the entanglement entropy between a spin and bosonic modes in a spin-boson model using different ground state ansatze. The entanglement entropy saturates exponentially to a constant as the value of the displacement parameters of the boson modes is increased. We also search for level crossings in a system composed of two spins coupled by a Dzyaloshinkskii-Moriya interaction.