Emergent Criticality and Friedan Scaling in a 2D Frustrated Heisenberg Antiferromagnet

Abstract

We study a two-dimensional frustrated Heisenberg antiferromagnet on the windmill lattice consisting of triangular and dual honeycomb lattice sites. In the classical ground state the spins on different sublattices are decoupled, but quantum and thermal fluctuations drive the system into a coplanar state via an "order from disorder" mechanism. We obtain the finite temperature phase diagram using renormalization group approaches. In the coplanar regime, the relative U$(1)$ phase between the spins on the two sublattices decouples from the remaining degrees of freedom, and is described by a six-state clock model with an emergent critical phase. At lower temperatures the system enters a ${\mathbb{Z}}_6$ broken phase with long-range phase correlations. We derive these results by two distinct renormalization group approaches to two-dimensional magnetism: by Wilson-Polyakov scaling and by Friedan's geometric approach to nonlinear sigma models where the scaling of the spin-stiffnesses is governed by the Ricci flow of a 4D metric tensor.

30 pages, 8 figures

References in corpus (12)

• Time-resolved Observation and Control of Superexchange Interactions with Ultracold Atoms in Optical Lattices
• Theory of Electron Nematic Order in LaOFeAs
• Ising and Spin orders in Iron-based Superconductors
• Formation of a Nematic Fluid at High Fields in Sr3Ru2O7
• Definitive Evidence for Order-by-Quantum-Disorder in Er2Ti2O7
• Manifestations of nematic degrees of freedom in the magnetic, elastic, and superconducting properties of the iron pnictides
• Quantum order by disorder and accidental soft mode Er2Ti2O7
• Interplay of quantum and thermal fluctuations in a frustrated magnet
• Octupolar ordering of classical kagome antiferromagnets in two and three dimensions
• Dipolar order by disorder in the classical Heisenberg antiferromagnet on the kagome lattice
• Ising transition in the two-dimensional quantum $J_1-J_2$ Heisenberg model
• Broken translational symmetry in an emergent paramagnetic phase of graphene

Cited by in corpus (9)

• Intertwined vestigial order in quantum materials: nematicity and beyond
• Emergent Potts Order in a Coupled Hexatic-Nematic XY model
• Emergent Power-Law Phase in the 2D Heisenberg Windmill Antiferromagnet: A Computational Experiment
• Diagnosing order by disorder in quantum spin systems
• Classical phase diagram of the stuffed honeycomb lattice
• Classical Heisenberg and planar spin models on the windmill lattice
• Three-state Potts nematic order in stacked frustrated spin models with SO(3) symmetry
• Quantum order by disorder in Frustrated Spin Nanotubes
• Phases and Phase Transitions of the Disordered Quantum Clock Model