Quantization of heat flow in the fractional quantum Hall regimeMitali BanerjeeDepartment of Physics, Columbia University, New York, NY, USATopological states of matter are characterized by topological invariants, which arephysical quantities whose values are quantized and do not depend on details of themeasured system. Among them the electrical Hall conductance, which is expressed inunits of e2/h, is easiest to probe. In the fractional quantum Hall effect regime, fractionalquantized values of the electrical Hall conductance attest to topologically ordered states,which are states that carry quasi-particles with fractional charge and (expected) anyonicstatistics. Another topological invariant, which is much harder to measure, is the thermalHall conductance, KT, expressed in units of ?0T=(?2kB2/3h)T. In 1D transport it does notdepend on the particles charge, particles exchange statistics, and is even insensitive to theinteraction strength among the particles. A fractional value of the quantized thermal Hallconductance shows that the probed state of matter is non-abelian. Quasiparticles in nonabelianstates may be useful for topological quantum computation. In this talk, I willreport our measurements of the thermal Hall conductance of the v=5/2 state to befractional, implying non-abelian nature of the state.