Many quantum spin liquids (QSLs) can be described using the Kitaev model on a honeycomb lattice. Because it can be used to describe an increasing number of materials, and because of the availability of an exact mathematical solution to the model, it is widely used in QSL research.

In Kitaev QSLs the magnetic excitations are known to break up (fractionalise) into Majorana fermions. While these exotic particles behave in the same way as the electrons in graphene, as described by the Dirac dispersion, they don't carry electric charge and are coupled to emergent gauge fields. The fractionalisation gives rise to characteristic continua in magnetic excitation spectra, as observed in various inelastic neutron-scattering experiments carried out at ISIS.

As a function of anisotropy, the Kitaev model undergoes a topological phase transition from a gapless to a gapped QSL state. This gapped state is related to the 'toric-code' model, which has applications in quantum computation and quantum error corrections.

The band structure of the Majorana fermions cannot be probed experimentally and so, in their recent publication in Physical Review Letters, Frank Kruger, a theorist at UCL and member of the Excitation Group at ISIS, and his PhD student Huanzhi Hu used theoretical calculations to investigate the nature of this phase transition.

They found that the topological phase transition becomes increasingly complex in any real material where additional magnetic interactions are present. While the transition shares hallmark features of quantum phase transitions in metals, such as non-Fermi liquid behaviour, the special properties of Majorana fermions make the transition different to those in electronic systems.

“This work is not only of fundamental theoretical importance, but it also makes experimental predictions, in particular regarding the expected signatures in inelastic neutron scattering experiments," explains Frank. 

The full paper can be found at DOI: 10.1103/PhysRevLett.133.146603