Thermal Hall conductivity near field-suppressed magnetic order in a Kitaev-Heisenberg model

We investigate thermal Hall conductivity κ_xy of a J-K Kitaev-Heisenberg model with a Zeeman field in the (111) direction in the light of the recent debate surrounding the possible re-emergence of Ising topological order (ITO) and half-quantized κ_xy/T upon field-suppression of long-range magnetic order in Kitaev materials. We use the purification-based finite temperature Tensor Network approach making no prior assumptions about the nature of the excitations: Majorana, visons or spin waves. For purely Kitaev interactions and fields h/K>0.02 sufficient to degrade ITO, the peak κ_xy/T monotonously decreases from half-quantization associated with lower fields - a behavior reminiscent of vison fluctuation corrections. In our J-K model (with ferro-K and antiferro-J), in the vicinity of field-suppressed magnetic order, we found κ_xy/T to be significant, with peak magnitudes exceeding half-quantization followed by a monotonous decrease with increasing h. We thus conclude that half-quantized thermal Hall effect, if found in our model in the vicinity of field suppressed magnetic order, is a fine-tuning effect and is not associated with a Majorana Hall state with ITO.