Nature of the Topological Transition of the Kitaev Model in [111] Magnetic Field

Abstract

We investigate the nature of the topological phase transition of the antiferromagnetic Kitaev model on the honeycomb lattice in the presence of a magnetic field along the [111] direction. The field opens a topological gap in the Majorana fermion spectrum and leads to a sequence of topological phase transitions before the field polarised state is reached. At mean field level the gap first closes at the three $M$ points in the Brillouin zone, where the Majorana fermions form Dirac cones, resulting in a change of Chern number by three. An odd number of Dirac fermions in the infrared is unusual and requires Berry curvature compensation in the UV, which occurs via topological, ring-like hybridisation gaps with higher-energy bands. We perform a renormalisation-group analysis of the topological phase transition at the three $M$ points within the Yukawa theory, allowing for intra- and inter-valley fluctuations of the spin-liquid bond operators. We find that the latter lead to a breaking of Lorentz invariance and hence a different universality compared to the standard Ising Gross-Neveu-Yukawa class.

10 pages, 6 figures

References in corpus (11)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• $\alpha$-RuCl3: a Spin-Orbit Assisted Mott Insulator on a Honeycomb Lattice
• Hyper-honeycomb iridate $\beta$-Li2IrO3 as a platform for Kitaev magnetism
• Long range magnetic ordering in Na${}_2$IrO${}_3$
• Critical flavour number of the Thirring model in three dimensions
• Possible Intermediate Quantum Spin Liquid Phase in $\alpha$-RuCl${}_3$ under High Magnetic Fields up to 100 T
• Emergent glassiness in disorder-free Kitaev model: Density matrix renormalization group study on a one-dimensional ladder setting
• Validity of SLAC fermions for the (1 + 1)-dimensional helical Luttinger liquid
• Caution on Gross-Neveu criticality with a single Dirac cone: Violation of locality and its consequence of unexpected finite-temperature transition
• Nature of Topological Phase Transition of Kitaev Quantum Spin Liquids