  Low-energy magnon bands in a two-dimensional spin ice model become integer
quantum magnon Hall bands. By calculating the localization length and the
two-terminal conductance of magnon transport, we show that the magnon bands
with disorders undergo a quantum phase transition from an integer quantum
magnon Hall regime to a conventional magnon localized regime. Finite size
scaling analysis as well as a critical conductance distribution shows that the
quantum critical point belongs to the same universality class as that in the
quantum Hall transition. We characterize thermal magnon Hall conductivity in
disordered quantum magnon Hall system in terms of robust chiral edge magnon
transport.
