Detection of symmetry-protected topological phases in one dimension with multiscale entanglement renormalization

2013/05/13 by Chang, Hsueh-Wen, Hsieh, Yun-Da, Kao, Ying-Jer
#FOS: Physical sciences #Strongly Correlated Electrons (cond-mat.str-el)

paper · doi:10.48550/arxiv.1305.2663

Abstract

Symmetry-protected topological (SPT) phases are short-range entangled quantum phases with symmetry, which have gapped excitations in the bulk and gapless modes at the edge. In this paper, we study the SPT phases in the spin-1 Heisenberg chain with a single-ion anisotropy D, which has a quantum phase transition between a Haldane phase and a large-D phase. Using symmetric multiscale entanglement renormalization ansatz (MERA) tensor networks, we study the nonlocal order parameters for time-reversal and inversion symmetry. For the inversion symmetric MERA, we propose a brick-and-rope representation that gives a geometrical interpretation of inversion symmetric tensors. Finally, we study the symmetric renormalization group (RG) flow of the inversion symmetric string-order parameter, and show that entanglement renormalization with symmetric tensors produces proper behavior of the RG fixed-points.

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