Symmetry-protected quantum state renormalization

Ching Yu Huang*, Xie Chen, Feng Li Lin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)


Symmetry-protected topological (SPT) phases with gapless edge excitations have been shown to exist in strongly interacting bosonic/fermionic systems and it is highly desirable to identify practical systems realizing such phases through numerical simulation. A central question to be addressed is how to determine the SPT order in the system given the simulation result, while no local order parameter can be measured to distinguish the phases from a trivial one. In the tensor network approach to simulate strongly interacting systems, the quantum state renormalization algorithm has been shown to be effective in identifying intrinsic topological orders. Here, we show that a modified algorithm can identify SPT orders by extracting the symmetry-protected fixed point entanglement pattern in the ground-state wave function, which is essential for the existence of SPT order. The key to this approach is to add proper symmetry protection to the renormalization process. We demonstrate the effectiveness of this algorithm with examples of nontrivial SPT phases with internal symmetry in 1D and internal and translation symmetry in 2D.

Original languageEnglish
Article number205124
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number20
Publication statusPublished - 2013 Nov 18

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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