Nonlocal string orders and entanglement spectrum in the spin-1/2 alternating Heisenberg-Ising chain

Abstract

By the infinite time-evolving block decimation (iTEBD) technique, the quantum phase transitions (QPTs) and the ground-state properties of a spin-1/2 alternating Heisenberg-Ising chain are investigated. As the Ising coupling is generalized into the ferromagnetic case (J I < 0), in addition to two well-known phases (the antiferromagnetic phase and the disordered dimer phase), an antiferromagnetic stripe phase is induced. Two QPTs at J I = ±2 can be described by the singular behavior of the bipartite entanglement entropy and the ground-state energy, and both are verified to be second-order transitions. Nonzero string orders (O s σ, σ = x, y, and z) and doubly degenerate entanglement spectra are observed in the disordered dimer phase, and these characters distinguish the disordered phase from other two phases. Especially, the string order introduced firstly to describe the Haldane phase of spin-1 chain is generalized to the spin-1/2 alternating Heisenberg-Ising chain.