Block-block entanglement and quantum phase transition in the spin-1/2 XX chain

The block-block entanglement in the ground state of spin-1/2 XX chain with three-spin and uniform long-range interactions among the z components of the spins is investigated. Our results show that the block-block entanglement manifests quantum phase transitions. Besides the logarithmic scaling behavior of the block-block entanglement with the block size, that is, S-L similar to log(2)(L), in phase I region, it is found that there is the power scaling behavior, S-L similar to L, in the quantum frustration regions. It is also found that the quantum frustration gives rise to an increase of block-block entanglement.