Numerical Study of Quantum Magnetism in Kitaev Material

In this talk, we will present a sign-problem free Monte Carlo study of quantum magnetism in the honeycomb Kitaev-Heisenberg model with external magnetic fields. We obtained the quantum critical points and finite temperature Berezinskii-Kosterlitz-Thouless transition between the magnetically (long-range or quasi-long-range) ordered phase to the spin polarized phase.