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arXiv:1412.7901 · Physical Review B

Topological order parameters of the spin- 12 dimerized Heisenberg ladder in magnetic field

Toshikaze Kariyado, Yasuhiro Hatsugai

Published Jun 8, 2015• 20 citations
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Abstract

Topological properties of the spin-1/2 dimerized Heisenberg ladder are investigated, focusing on the plateau phase in the magnetic field whose magnetization is half of the saturation value. Although the applied magnetic field removes most of the symmetries of the system, there is a symmetry-protected topological phase supported by the spatial inversion symmetry. The ${Z}_{2}$ Berry phase associated with a symmetry-respecting boundary and quantized into 0 and $\ensuremath{\pi}$ is used as a symmetry-protected topological order parameter. Edge states are also analyzed to confirm the bulk-edge correspondence. In addition, a symmetry-breaking boundary is considered. Then, we observe a different type of quantization of the Berry phase, i.e., a quantization into $\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2$ of the Berry phase. In this case, the bulk-edge correspondence is also different, namely, there emerge ``polarized'' edge states for the case with $\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2$ quantization. We also evaluate the entanglement entropy by the infinite time-evolving block decimation (iTEBD) to complement the Berry-phase-based arguments. Further, a different type of the topological order parameter is extracted from the matrix product state representation of the ground state given by the iTEBD.

DOI
10.1103/physrevb.91.214410

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Topological properties of the spin-1/2 dimerized Heisenberg ladder are investigated, focusing on the plateau phase in the magnetic field whose magnetization is half of the saturation value. Although the applied magnetic field removes most of the symmetries of the system, there is a symmetry-protected topological phase supported by the spatial inversion symmetry. The Z2{Z}_{2}Z2​ Berry phase associated with a symmetry-respecting boundary and quantized into 0 and \ensuremathπ\ensuremath{\pi}\ensuremathπ is used as a symmetry-protected topological order parameter. Edge states are also analyzed to confirm the bulk-edge correspondence. In addition, a symmetry-breaking boundary is considered. Then, we observe a different type of quantization of the Berry phase, i.e., a quantization into \ifmmode±\else\textpm\fi\ensuremathπ/2\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2\ifmmode±\else\textpm\fi\ensuremathπ/2 of the Berry phase. In this case, the bulk-edge correspondence is also different, namely, there emerge ``polarized'' edge states for the case with \ifmmode±\else\textpm\fi\ensuremathπ/2\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2\ifmmode±\else\textpm\fi\ensuremathπ/2 quantization. We also evaluate the entanglement entropy by the infinite time-evolving block decimation (iTEBD) to complement the Berry-phase-based arguments. Further, a different type of the topological order parameter is extracted from the matrix product state representation of the ground state given by the iTEBD.
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