Thermal Hall Conductivity of a Kitaev-Heisenberg Model and a Zeeman Field

Absence of thermal Hall half-quantization by field-suppression of magnetic order in a Kitaev-Heisenberg model

We investigate thermal hall conductivity of a kitaev-heisenberg model and a zeeman field in the direction in the light of the recent debate surrounding the possible re-emergence of ising topological order and half-quantized upon field-suppression of long-range magnetic order in kitaev materials.We use the purification-based finite temperature tensor network approach making no priorassumptions about the nature of the excitations: majorana, visons or spinwaves.In the model and in the vicinity of field-suppressed magnetic order, we found the peak magnitudes exceeding half-quantization followed by a decrease with increasing fields-a behavior physically consistent with vison fluctuation corrections and qualitatively different from spin wave treatments.We thus conclude that half-quantized thermal hall effect, if observed in the vicinity of field suppressed magnetic order in ourmodel, is a fine-tuning effect and is not associated with a majorana hall state with ising topological order.