Block-block entanglement and quantum phase transitions in the one-dimensional extended Hubbard model

In this paper, we study block-block entanglement in the ground state of a one-dimensional extended Hubbard model. Our results show that the phase diagram derived from the block-block entanglement manifests a richer structure than that of the local (single-site) entanglement because it comprises nonlocal correlation. Besides phases characterized by the charge-density wave, the spin-density wave, and phase separation, which can be sketched out by the local entanglement, singlet superconductivity phase could be identified on the contour map of the block-block entanglement if the block size is larger than 1. Scaling analysis shows that log(2)(l) behavior of the block-block entanglement may exist in both the noncritical and critical regions, while some local extremum are induced by the finite-size effect. We also study the block-block entanglement defined in the momentum space and discuss its relation to the phase transition from singlet superconducting state to the charge-density-wave state.