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

We investigate thermal Hall conductivity k(xy) of a J-K Kitaev-Heisenberg model with a Zeeman field in the (111) direction in light of the recent debate surrounding the possible reemergence of Ising topological order (ITO) and half-quantized K-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 greater than or similar to 0.02 sufficient to degrade ITO, the peak k(xy)/T monotonically decreases from half quantization associated with lower fields-a behavior reminiscent of vison fluctuation corrections. For higher fields h/K greater than or similar to 0.1, we find the results qualitatively consistent with a spin-wave treatment. In our J-K model (with ferro-K and antiferro-J), in the vicinity of field-suppressed magnetic order, we found k(xy)/T to be significant, with peak magnitudes exceeding half quantization followed by a monotonic decrease with increasing h. We thus conclude that the half-quantized thermal Hall effect in the vicinity of field-suppressed magnetic order in our model is a fine-tuning effect and is not associated with a Majorana Hall state with ITO.

Automated summary

We investigate the thermal Hall conductivity k(xy) in a J-K Kitaev-Heisenberg model with a Zeeman field in the (111) direction, to understand the relationship between the possible reemergence of Ising topological order (ITO) and the half-quantized K-xy/T upon field suppression of long-range magnetic order in Kitaev materials. We use a purification-based finite-temperature tensor network approach without assuming the nature of the excitations: Majorana, visons, or spin waves. Our results show that the half-quantized thermal Hall effect near field-suppressed magnetic order is a fine-tuning effect and is not associated with a Majorana Hall state with ITO.