Reduction and emergence in the fractional quantum Hall state

• The fractional quantum Hall effect is presented as an emergent phenomenon in physics.
• The emergence is not based on symmetry breaking but on topological effects.
• Topological order is understood in terms of long-range quantum entanglement.
• The system is a holistic entity, understood via a modification of Humphreys’ fusion.

We present the fractional quantum Hall (FQH) effect as a candidate emergent phenomenon. Unlike some other putative cases of condensed matter emergence (such as thermal phase transitions), the FQH effect is not based on symmetry breaking. Instead FQH states are part of a distinct class of ordered matter that is defined topologically. Topologically ordered states result from complex long-ranged correlations between their constituent parts, such that the system displays strongly irreducible, qualitatively novel properties.