SciPost Physics

SciPost Phys. 10, 033 (2021) · published 12 February 2021

• doi: 10.21468/SciPostPhys.10.2.033
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Abstract

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 N\'{e}el 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.

• Parisen Toldin, Boundary Critical Behavior of the Three-Dimensional Heisenberg Universality Class
  Phys. Rev. Lett. 126, 135701 (2021) [Crossref]
• Roberts et al., One-dimensional model for deconfined criticality with Z3×Z3 symmetry
  Phys. Rev. B 103, 155143 (2021) [Crossref]
• Tantivasadakarn et al., Building models of topological quantum criticality from pivot Hamiltonians
  SciPost Phys. 14, 013 (2023) [Crossref]
• Metlitski, Boundary criticality of the O(N) model in d = 3 critically revisited
  SciPost Phys. 12, 131 (2022) [Crossref]
• Zhang et al., Surface criticality of the antiferromagnetic Potts model
  Phys. Rev. B 105, 224415 (2022) [Crossref]
• Lee et al., Quantum Criticality Under Decoherence or Weak Measurement
  PRX Quantum 4, 030317 (2023) [Crossref]
• Yu et al., Conformal Boundary Conditions of Symmetry-Enriched Quantum Critical Spin Chains
  Phys. Rev. Lett. 129, 210601 (2022) [Crossref]
• Sun et al., Quantum extraordinary-log universality of boundary critical behavior
  Phys. Rev. B 106, 224502 (2022) [Crossref]
• Ma et al., Edge physics at the deconfined transition between a quantum spin Hall insulator and a superconductor
  SciPost Phys. 12, 196 (2022) [Crossref]
• Xu et al., Interaction-Driven Metal-Insulator Transition with Charge Fractionalization
  Phys. Rev. X 12, 021067 (2022) [Crossref]
• Liu et al., Magnetic impurities at quantum critical points: Large- N expansion and connections to symmetry-protected topological states
  Phys. Rev. B 104, 104201 (2021) [Crossref]
• Sun et al., Classical-quantum correspondence of special and extraordinary-log criticality: Villain's bridge
  Phys. Rev. B 106, 174516 (2022) [Crossref]
• Xu et al., Deconfined quantum critical point with nonlocality
  Phys. Rev. B 106, 155131 (2022) [Crossref]
• Ding et al., Special transition and extraordinary phase on the surface of a two-dimensional quantum Heisenberg antiferromagnet
  SciPost Phys. 15, 012 (2023) [Crossref]
• Wang et al., Extraordinary surface critical behavior induced by the symmetry-protected topological states of a two-dimensional quantum magnet
  Phys. Rev. B 108, 014409 (2023) [Crossref]
• Krishnan et al., A plane defect in the 3d O(N) model
  SciPost Phys. 15, 090 (2023) [Crossref]
• Xu et al., Persistent corner spin mode at the quantum critical point of a plaquette Heisenberg model
  Phys. Rev. B 106, 214409 (2022) [Crossref]
• Wu et al., Continuous Phase Transitions between Fractional Quantum Hall States and Symmetry-Protected Topological States
  Phys. Rev. Lett. 131, 256502 (2023) [Crossref]
• Parisen Toldin et al., Boundary Criticality of the 3D O( N ) Model: From Normal to Extraordinary
  Phys. Rev. Lett. 128, 215701 (2022) [Crossref]
• Padayasi et al., The extraordinary boundary transition in the 3d O(N) model via conformal bootstrap
  SciPost Phys. 12, 190 (2022) [Crossref]
• Parisen Toldin, Surface critical behavior of the three-dimensional O(3) model
  J. Phys.: Conf. Ser. 2207, 012003 (2022) [Crossref]
• Zhang et al., Sublattice extraordinary-log phase and special points of the antiferromagnetic Potts model
  Phys. Rev. B 108, 024402 (2023) [Crossref]
• Wang et al., Bulk and surface critical behavior of a quantum Heisenberg antiferromagnet on two-dimensional coupled diagonal ladders
  Phys. Rev. B 106, 134407 (2022) [Crossref]
• Parisen Toldin, The ordinary surface universality class of the three-dimensional O(N) model
  Phys. Rev. B 108, L020404 (2023) [Crossref]