Tensor network studies of thermal Hall transport in Kitaev-Heisenberg model.

The honeycomb lattice Mott insulating systems such as α–RuCl₃, have emerged as candidates for realizing the Kitaev spinons. Motivated by the experimental observation of quantized (likely half-integer) thermal Hall conductivity α–RuCl₃, we study the thermal Hall conductivity of a nonintegrable Kitaev-Heisenberg model numerically, using tensor network techniques. Our tensor network analysis uses the purification method to represent mixed quantum states at finite temperature as pure states on an enlarged Hilbert space carrying both phyical and ancilla sites. We compare our findings with reported quantized thermal Hall conductivity results. We also study the topological entanglement entropy - a measure of topological order - as a function of the model parameters. Our study confirms continued persistence of topological order deep in the spin density wave order phase.