Coherent spinon behaviour in quantum spin liquids at finite temperature

Realistic Hamiltonians for quantum spin liquids often exhibit a large separation of energy scales between their elementary excitations. At experimentally relevant temperatures, some excitations are in a low-temperature regime where they are sparse and hop coherently across the lattice, while others are thermally excited and behave as a dense, stochastic ensemble. We study the interplay of these quasiparticles in the case where it is driven solely by their nontrivial mutual statistics rather than by direct interaction energy terms. We consider toy models for Z2 quantum spin liquids, where the two species of excitation (dubbed spinons and visons) are mutual semions. The nontrivial statistical angle between the two species leads to interference effects that we study using a combination of numerical and analytical tools. In the limit of self-retracing paths, we are able to use a Bethe lattice approximation to construct exact analytical expressions for the time evolution of the site-resolved density profile of a spinon initially confined to a single site. We also highlight an intriguing feedback mechanism, akin to the Nagaoka effect, whereby the spinons become localised on patches of expelled incoherent visons, the typical diameter of which increases as temperature is reduced.