Block Entanglement in the Single-Hole Hubbard Model

We investigate the distribution of the entanglement of the one-dimensional single-hole Hubbard model (HM) and study the relationship between the entanglement and quantum phase transition in the model. The von Neumann entropy of a block with neighbouring spins L for a single-hole HM is calculated using the density-matrix renormalization group. The distributions of the entanglement entropy in the ground state, as a function of block length, show a dramatic effect, i.e. effectively decoupling with the centres, no matter how the Coulomb interaction u>0 or u<0. Contrarily, for the Coulomb interaction u=0 or close to zero, the entanglement entropy in the single-hole model reaches a saturation value for a certain block size. For a fixed size L=40, the ground state entanglement entropy measure, as a function of u, shows a peak corresponding to the critical quantum phase transition.