Quantum phase transitions and hidden topological order in one-dimensional S=1 Heisenberg–Ising alternating model

Abstract

By the infinite time-evolving block decimation method, the ground state properties of the =1 Heisenberg–Ising alternating chain have been investigated in the thermodynamic limit. A ground-state phase diagram, which includes three different phases, i.e., an antiferromagnetic strip phase, a dimer phase, and an antiferromagnetic phase, is obtained. A modified definition of the string order is adopted to describe the dimer phase, and it is found to have nonzero antiferromagnetic topological string order. The quantum phase transitions (QPTs) in such a model can be well described by the singularities of bipartite entanglement and fidelity bifurcations, and two second-order QPTs points are determined to be at . The central charges at both QPTs points are determined to be 1/2. Therefore, both QPTs belong to the Ising universality class with central charges 1/2.