Boundary phase transitions of two-dimensional quantum critical XXZ model

Abstract

The boundary critical behavior of the two-dimensional (2D) quantum antiferromagnetic (AF) XXZ model coupled with either a dangling spin-1/2 XXZ chain or a dangling two-leg ladder on the boundary is studied with the bosonization and renormalization group analysis. A rich boundary phase diagram is obtained in each case. In the dangling chain case, the boundary either develops a long-range AF order in the easy-plane or the easy-axis direction with extraordinary critical behavior, or has a valence bond solid order with ordinary boundary critical behavior. In the case of a dangling two-leg ladder, besides the possible easy-plane or easy-axis AF ordered phases on the boundary with extraordinary critical behavior, the boundary can form a singlet phase with ordinary critical behavior without breaking any symmetry. These results are consistent with recent numerical simulations on the boundary critical behavior of 2D quantum spin models.

21 pages, 5 figures

References in corpus (13)

• 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
• Conformal Boundary Conditions of Symmetry-Enriched Quantum Critical Spin Chains
• Boundary Criticality of the 3D O($N$) Model: From Normal to Extraordinary
• Surface critical behaviors of coupled Haldane chains
• Extraordinary-log surface phase transition in the three-dimensional $XY$ model
• Continuous Néel-VBS Quantum Phase Transition in Non-Local one-dimensional systems with SO(3) Symmetry
• Surface criticality of antiferromagnetic Potts model
• Spin vs. bond correlations along dangling edges of quantum critical magnets
• Extraordinary-log Universality of Critical Phenomena in Plane Defects
• Special Transition and Extraordinary Phase on the Surface of a Two-Dimensional Quantum Heisenberg Antiferromagnet
• Gapless edge states and their stability in two-dimensional quantum magnets
• Sublattice extraordinary-log phase and new special point of the antiferromagnetic Potts model

Cited by in corpus (1)

• Boundary Renormalization Group Flow of Entanglement Entropy at a (2+1)-Dimensional Quantum Critical Point