Topological Excitations and the Dynamic Structure Factor of Spin Liquids on the Kagome Lattice

April 1, 2014
ac, Plots of S(k,ω) at zero temperature for different spinon–vison interaction strengths as a function of frequency and momentum along the high-symmetry directions between the Γ, M and K points of the extended Brillouin zone, indicated by the blue arrows in e. a, Non-interacting spinons. Note that in the Q1=Q2 state two of the three spinon bands are degenerate, whereas the third, highest energy spinon band is flat. This flat spinon band gives rise to the horizontal feature at ω0.75J. b,  Spinon–vison interaction g0=0.2. c, Spinon–vison interaction g0=0.6. d,eS(k,ω) for non-interacting spinons at fixed frequency ω/J=0.4 (d) and ω/J=0.85 (e). The elementary Brillouin zone of the kagome lattice is indicated by a dashed hexagon in e. Note the sharp onset of the two-spinon continuum for non-interacting spinons in a and d, which is washed out when interactions with visons are accounted for. All data in this figure were calculated for |Q1|=0.4 and the spinon gap was fixed at Δs0.05J. The vison gap is set to Δv=0.025J in b and c.  [Figure reprinted by permission from Macmillan Publishers Ltd: Nature ©2014.]

Recent neutron scattering experiments on the spin-1/2 kagome lattice antiferromagnet ZnCu3(OH)6Cl2 (Herbertsmithite) provide the first evidence of fractionalized excitations in a quantum spin liquid state in two spatial dimensions. In contrast to existing theoretical models of both gapped and gapless spin liquids, which give rise to sharp dispersing features in the dynamic structure factor, the measured dynamic structure factor reveals an excitation continuum that is remarkably flat as a function of frequency.

In a Letter in Nature Physics, Matthias Punk, Debanjan Chowdhury, and Prof. Subir Sachdev show that many experimentally observed features can be explained by the presence of topological vison excitations in a Z2 spin liquid. These visons form flat bands on the kagome lattice, and thus act as a momentum sink for spin-carrying excitations that are probed by neutron scattering. The authors compute the dynamic structure factor for two different Z2 spin liquids and find that the results for one of them are in qualitative agreement with the neutron scattering experiments above a very low energy cutoff, below which the structure factor is probably dominated by impurities. (See Nature Physics 10, 289–293 (2014) | doi:10.1038/nphys2887.