Statistics of Fractionalized Excitations through Threshold Spectroscopy

We show that neutral anyonic excitations have a signature in spectroscopic measurements of materials: The low-energy onset of spectral functions near the threshold follows universal power laws with an exponent that depends only on the statistics of the anyons. This provides a route, using experimental techniques such as neutron scattering and tunneling spectroscopy, for detecting anyonic statistics in topologically ordered states such as gapped quantum spin liquids and hypothesized fractional Chern insulators. Our calculations also explain some recent theoretical results in spin systems.

Figure 1

(a) In phases with topological order, scattering processes can create fractionalized anyonic excitations above some threshold energy. (b) The statistics of the excitations mediate long-range effects between them.

Figure 2

(a) Two-particle spectral function from exact diagonalization on a $600\times 600$ square lattice for fermions with nearest-neighbor repulsion $U$ and next-nearest-neighbor repulsion $V$. The high-energy behavior is drastically affected by interactions, but the low-energy linear onset is unchanged as seen in the log-log plot on the top right, where the exponents for all three cases is 0.95. (c) $S(0,\omega )$ for noninteracting bosons ($b$), semions ($s$), fermions ($f$), and hard-core bosons (hcb) on a $20\times 20$ lattice. (d) Density of states for bosons and fermions.