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A series of symmetry-protected topological(SPT) and trivial spin-gap phasesin the spin-1/2 ferromagnetic--antiferromagnetic alternating Heisenberg chainwith alternating next-nearest-neighbour interaction are investigated using twokinds of entanglement spectra defined by different divisions of the wholechain. In the case one of the next-nearest-neighbor interaction vanishes, themodel reduces to the $\Delta$-chain in which a series of spin-gap phases arefound in J. Phys. Soc. Jpn. 77, 044707 (2008). From the degeneracy of theentanglement spectra, these phases are identified as the SPT and trivialphases. It is found that the ground state phases boundaries are insensitive tothe strength of the alternation in next-nearest neighbor interaction. Theseresults are consistent with the analysis based on the nonlinear $\sigma$ modeland exact solution on the ferromagnetic-nonmagnetic phase boundary.

Topological Phases of Spin-1/2 Ferromagnetic--Antiferromagnetic Alternating Heisenberg Chains with Alternating Next-Nearest-Neighbour Interaction