Four interacting spins: Addition of angular momenta, spin–spin correlation functions, and entanglement

Abstract

We study four spins on a ring coupled through competing Heisenberg interactions between nearest neighbors, J, and next-nearest neighbors, J2≡αJ>0. From the pedagogical point of view, dealing with few spins illustrates how to add more than two angular momenta in a systematic way. The spectrum is obtained by using the rules for addition of four angular momenta, which allows us to follow the evolution of the ground state with α, characterized by level crossings and by spin–spin correlation functions. The reduced number of spins also allows us to illustrate how to quantify bipartite entanglement.