Quantum entanglement in the S=1/2 spin ladder with ring exchange

In this paper we study the concurrence and the block-block entanglement in an S=1/2 spin ladder with four-spin ring exchange by the exact diagonalization method of finite clusters of spins. The relation between the global phase diagram and the ground-state entanglement is investigated. It is shown that block-block entanglement of different block sizes and geometry manifests richer information about the system. We find that the extremal point of the two-site block-block entanglement on the rung locates a transition point exactly due to SU(4) symmetry at this point. The scaling behavior of the block-block entanglement is discussed. Our results suggest that the block-block entanglement can be used as a convenient marker of the quantum phase transition in some complex spin systems.