The quantum spin chains of Temperley–Lieb type and the topological basis states

Abstract

In this paper, based on the usual spin basis, we present a complete orthonormal basis with the single loop $$d=\sqrt{2}$$ consisting of maximally entangled four-qubit states. Then we investigate the particular physical properties of the topological basis states in the corresponding quantum spin chains of Temperley---Lieb type. Whether the system is the anti-ferromagnetic case or the ferromagnetic case, the ground states are all doubly degenerate, and they all fall on the topological basis states. Furthermore, we introduce the Yangian $$Y(sl(2))$$ operators to investigate the transitions between the quantum states.