Nature of the topological transition of the Kitaev model in [111] magnetic field

We investigate the nature of the topological phase transition of the antiferromagnetic Kitaev model on a 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-polarized state is reached. At mean-field level, the gap first closes at the three <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mi>M</a:mi> </a:math> 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 infrared is unusual and requires Berry curvature compensation in ultraviolet, which occurs via topological, ringlike hybridization gaps with higher-energy bands. We perform a renormalization-group analysis of the topological phase transition at the three <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mi>M</b:mi> </b:math> points within the Yukawa theory, allowing for intravalley and intervalley 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 with the standard Ising Gross-Neveu-Yukawa class.