2020/04/30 by Chao-Ming Jian, Yichen Xu, Xiao-Chuan Wu +1
Physics and Astronomy · #Boundary (topology) #Boundary conformal field theory #Boundary value problem #Phase transition #Physics of Superconductivity and Magnetism #Quantum #Quantum critical point #Quantum many-body systems #Quantum phase transition #Quantum phases #Symmetry (geometry) #Topological Materials and Phenomena #Valence bond theory #cond-mat.str-el
paper · pdf · doi:10.21468/scipostphys.10.2.033
published as SciPost Phys. 10, 033 (2021) · 7 pages, 3 figures
openalex created_date 2020/04/24 · arxiv created 2020/12/13 · openalex publication_date 2021/02/12 · arxiv updated 2021/02/16 · openalex updated_date 2026/08/06
One dimensional (1d) interacting systems with local Hamiltonians can be studied with various well-developed analytical methods. Recently novel 1d physics was found numerically in systems with either spatially nonlocal interactions, or at the 1d boundary of 2d quantum critical points, and the critical fluctuation in the bulk also yields effective nonlocal interactions at the boundary. This work studies the edge states at the 1d boundary of 2d strongly interacting symmetry protected topological (SPT) states, when the bulk is driven to a disorder-order phase transition. We will take the 2d Affleck-Kennedy-Lieb-Tasaki (AKLT) state as an example, which is a SPT state protected by the SO(3) spin symmetry and spatial translation. We found that the original (1+1)d boundary conformal field theory of the AKLT state is unstable due to coupling to the boundary avatar of the bulk quantum critical fluctuations. When the bulk is fixed at the quantum critical point, within the accuracy of our expansion method, we find that by tuning one parameter at the boundary, there is a generic direct transition between the long range antiferromagnetic Néel order and the valence bond solid (VBS) order. This transition is very similar to the Néel-VBS transition recently found in numerical simulation of a spin-1/2 chain with nonlocal spatial interactions. Connections between our analytical studies and recent numerical results concerning the edge states of the 2d AKLT-like state at a bulk quantum phase transition will also be discussed.