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Topological properties of the spin-1/2 dimerized Heisenberg ladder areinvestigated focusing on the plateau phase in the magnetic field whosemagnetization is half of the saturation value. Although the applied magneticfield removes most of the symmetries of the system, there is a symmetryprotected topological phase supported by the spatial inversion symmetry. TheZ_2 Berry phase associated with a symmetry respecting boundary and quantizedinto 0 and \pi is used as a symmetry protected topological order parameter.Edge states are also analyzed to confirm the bulk-edge correspondence. Inaddition, a symmetry breaking boundary is considered. Then, we observe a uniquetype of quantization of the Berry phase, a quantization into +-\pi/2 of theBerry phase. In this case, the bulk-edge correspondence is also unique, namely,there emerge "polarized" edge states for the case with +-\pi/2 quantization. Wealso evaluate the entanglement entropy by the infinite time-evolving blockdecimation (iTEBD) to complement the Berry phase based arguments. Further, adifferent type of the topological order parameter is extracted from the matrixproduct state representation of the ground state given by the iTEBD.

Topological Order Parameters of the Spin-1/2 Dimerized Heisenberg Ladder in Magnetic Field