Doubly degenerate entanglement spectrum and nonzero string order in the spin-1/2 Heisenberg-Ising chain

The ground-state properties and quantum phase transitions (QPTs) in spin-1/2 Heisenberg-Ising alternating chain has been investigated by the iTEBD algorithm. Four different ground-state phases, i.e., a ferromagnetic phase (FM), an antiferromagnetic phase (AF), a stripe phase (SP), and a disordered phase were distinguished. The disordered phase, which has nonzero string orders and the doubly degenerate entanglement spectrum, was observed as Heisenberg coupling JH>0.5. The disordered phase in such a model is found to belong to the same topological phase as the Haldane state. In the disordered phase, every two nearest-neighbor spin-1/2 spins connected by the Ising coupling behave like an integer (S=1) spin. Furthermore, the QPTs from the disordered phase to the AF and SP phases belong to the Ising universality class with central charges c=c¯=1/2.