Critical-entanglement spectrum of one-dimensional symmetry-protected topological phases

2014/06/30 by Wen-Jia Rao, Xin Wan, Guang-Ming Zhang · 1 citation
Physics and Astronomy · #Condensed matter physics #Critical point (mathematics) #Delocalized electron #Ising model #Phase transition #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Square lattice #Topological Materials and Phenomena #Topological order #cond-mat.stat-mech #cond-mat.str-el #quant-ph

paper · pdf · doi:10.1103/physrevb.90.075151

published as Phys. Rev. B 90, 075151 (2014) · 5 pages, 5 figures; publication version

openalex publication_date 2014/08/28 · arxiv created 2014/09/01 · arxiv updated 2014/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Under an appropriate symmetric extensive bipartition in a one-dimensional symmetry-protected topological (SPT) phase, a bulk critical-entanglement spectrum can be obtained, resembling the excitation spectrum of the critical point separating the SPT phase from the trivial (vacuum) state. Such a critical point is beyond the standard Landau-Ginzburg-Wilson paradigm for symmetry-breaking phase transitions. For the S=1 SPT (Haldane) phase with the Affleck-Kennedy-Lieb-Tasaki exact wave function, the resulting critical-entanglement spectrum has a residual entropy per lattice site s_r=0.67602, showing a delocalized version of the edge excitations in the SPT phase. From the wave function corresponding to the lowest entanglement energy level, the central charge of the critical point can be extracted c\ensuremath≈1.01\ifmmode±\else\textpm\fi0.01. The critical theory can be identified as the same effective field theory as the spin-1/2 antiferromagnetic Heisenberg chain or the spin-1/2 Haldane-Shastry model with inverse-square long-range interaction.

Citations

• Critical theory of quantum spin chains
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Detecting Topological Order in a Ground State Wave Function
• Collective States of Interacting Anyons, Edge States, and the Nucleation of Topological Liquids
• Entanglement spectrum of a topological phase in one dimension
• Nonlinear Field Theory of Large-Spin Heisenberg Antiferromagnets: Semiclassically Quantized Solitons of the One-Dimensional Easy-Axis Néel State
• Continuum dynamics of the 1-D Heisenberg antiferromagnet: Identification with the O(3) nonlinear sigma model

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