  We present a theory of the thermal Hall effect in insulating quantum magnets,
where the heat current is totally carried by charge-neutral objects such as
magnons and spinons. Two distinct types of thermal Hall responses are
identified. For ordered magnets, the intrinsic thermal Hall effect for magnons
arises when certain conditions are satisfied for the lattice geometry and the
underlying magnetic order. The other type is allowed in a spin liquid which is
a novel quantum state since there is no order even at zero temperature. For
this case, the deconfined spinons contribute to the thermal Hall response due
to Lorentz force. These results offer a clear experimental method to prove the
existence of the deconfined spinons via a thermal transport phenomenon.
