Entanglement and topological order in 1D and 2D systems

Abstract: In this talk, we discuss about the possible definition of quantum topological order and its relationship with quantum entanglement. In showing the character of the particular quantum phase, we use the particular examples of 1D and 2D exactly soluble models, including XX-model, 1D and 2D cluster state, Kitaev toric code model and Wen’s model. Through the complete analytic solution of the systems and the structure of total eigenstates, we clarify the vaguely existing notion of quantum phase transition and topological order as well as the implication of their use for quantum computation.