Measuring the Boundary Gapless State and Criticality via Disorder Operator

Abstract

The disorder operator is often designed to reveal the conformal field theory information in quantum many-body systems. By using large-scale quantum Monte Carlo simulation, we study the scaling behavior of disorder operators on the boundary in the two-dimensional Heisenberg model on the square-octagon lattice with gapless topological edge state. In the Affleck-Kennedy-Lieb-Tasaki phase, the disorder operator is shown to hold the perimeter scaling with a logarithmic term associated with the Luttinger liquid parameter K. This effective Luttinger liquid parameter K reflects the low-energy physics and CFT for (1+1)D boundary. At bulk critical point, the effective K is suppressed but keeps finite value, indicating the coupling between the gapless edge state and bulk fluctuation. The logarithmic term numerically captures this coupling picture, which reveals the (1+1)D SU(2)1 CFT and (2+1)D O(3) CFT at boundary criticality. Our Letter paves a new way to study the exotic boundary state and boundary criticality.

8 Pages,7 figures

References in corpus (36)

• Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Stochastic series expansion method with operator-loop update
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Computational Studies of Quantum Spin Systems
• A symmetry principle for Topological Quantum Order
• Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
• Algebraic higher symmetry and categorical symmetry -- a holographic and entanglement view of symmetry
• Ground-state fidelity in one-dimensional gapless model
• Ground states of a frustrated quantum spin chain with long-range interactions
• Scaling of entanglement entropy at deconfined quantum criticality
• Surface and bulk transitions in three-dimensional O(n) models
• Disorder Operators and their Descendants
• Unconventional Surface Critical Behaviors Induced by Quantum Phase Transition from Two-Dimensional Affleck-Kennedy-Lieb-Tasaki Phase to Néel Order
• Boundary critical behavior of the three-dimensional Heisenberg universality class
• Scaling of disorder operator at deconfined quantum criticality
• Triangular lattice quantum dimer model with variable dimer density
• Universal Features of Higher-Form Symmetries at Phase Transitions
• Engineering Surface Critical Behavior of (2+1)-Dimensional O(3) Quantum Critical Points
• Higher-form symmetry breaking at Ising transitions
• Spectroscopic signatures of crystal momentum fractionalization
• Nonordinary criticality at the edges of planar spin-1 Heisenberg antiferromagnets
• Fermion disorder operator at Gross-Neveu and deconfined quantum criticalities
• Scaling of disorder operator at $(2+1)d$ U(1) quantum criticality
• Surface critical behaviors of coupled Haldane chains
• Emergent glassy behavior in a kagome Rydberg atom array
• Quantum Spin Liquid with Even Ising Gauge Field Structure on Kagome Lattice
• Extraordinary-log surface phase transition in the three-dimensional $XY$ model
• Topological phase transition and single/multi anyon dynamics of $Z_2$ spin liquid
• Nonordinary edge criticaliy of two-dimensional quantum critical magnets
• Continuous Néel-VBS Quantum Phase Transition in Non-Local one-dimensional systems with SO(3) Symmetry
• Disorder Operator and Rényi Entanglement Entropy of Symmetric Mass Generation
• Bulk and edge dynamics of a 2D Affleck-Kennedy-Lieb-Tasaki model
• Special Transition and Extraordinary Phase on the Surface of a Two-Dimensional Quantum Heisenberg Antiferromagnet
• Extraordinary surface critical behavior induced by symmetry-protected topological state of a two-dimensional quantum magnet

Cited by in corpus (3)

• Addressing general measurements in quantum Monte Carlo
• Worldline deconfinement and emergent long-range interaction in the entanglement Hamiltonian and in the entanglement spectrum
• Exploring the limit of the Lattice-Bisognano-Wichmann form describing the Entanglement Hamiltonian: A quantum Monte Carlo study