Doubly degenerate entanglement spectrum and entanglement plateau in the S=1 bond-alternating chain

Quantum entanglement, entanglement spectrum, magnetization, and ground-state energy of the S=1 bond-alternating antiferromagnetic Heisenberg chain under magnetic field are investigated by the infinite time-evolving block decimation (iTEBD) method. Bipartite entanglement and entanglement spectrum are found to be capable of describing all the quantum phase transitions (QPTs). A rich ground-state phase diagram, which comprises of five different phases, i.e., a singlet-dimer phase, a Haldane phase, a Tomonaga-Luttinger liquid (TLL) phase, a 1/2 plateau phase, and a saturated ferromagnetic phase, is determined. It is interesting that, with the appearance of magnetization plateaus, entanglement plateaus are observed simultaneously. In the Haldane phase, doubly degenerate entanglement spectra on both even and odd bonds are observed. However, in the 1/2 plateau phase, only the entanglement spectra on the even bonds are found to be doubly degenerated.