Matrix product state approach to a frustrated spin chain with long-range interactions

We make extensive simulations over a spin chain model that combines the frustrated J(1) - J(2) spin chain and the long-range nonfrustrated (-1)((r-1))r(-alpha) decay interactions through the variational matrix product state method for both finite and infinite lengths. We study both the ground-state entanglement and phase diagram. We find that it is most entangled in the rotation invariant long-range ordered antiferromagnetic phase, where the entanglement scales approximately logarithmically. We determine the development of the Majudar-Ghosh point to a disorder line from entanglement. And we approximately determine the transition from the dimerized and incommensurate phase of the J(1) - J(2) model to a decoupled phase by studying spin correlation and the dimerization order parameter. Some implications for entanglement in systems with long-range interactions are stated.