Quantum spin liquids are long-range entangled states of matter with emergent gauge fields and fractionalized excitations. While candidate materials, such as the Kitaev honeycomb ruthenate $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$, show magnetic order at low temperatures
T, here we demonstrate numerically a dynamical crossover from magnonlike behavior at low
T and frequencies $\ensuremath{\omega}$ to long-lived fractionalized fermionic quasiparticles at higher
T and $\ensuremath{\omega}$. This crossover is akin to the presence of spinon continua in quasi-1D spin chains. It is further shown to go hand in hand with persistent typicality down to very low
T. This aspect, which has also been observed in the spin-1/2 kagome Heisenberg antiferromagnet, is a signature of proximate spin liquidity and emergent gauge degrees of freedom more generally, and can be the basis for the numerical study of many finite-
T properties of putative spin liquids.
In quantum spin liquid states, the fractionalized spinon excitations can carry fractional crystal symmetry quantum numbers, and this symmetry fractionalization distinguishes different symmetry-enriched spin liquid states with identical intrinsic topological order. In this work we propose a simple way to detect signatures of such crystal symmetry fractionalizations from the crystal symmetry representations of the ground state wave function. We demonstrate our method on projected
Z2 spin liquid wave functions on the kagome lattice, and show that it can be used to classify generic wave functions. Particularly our method can be used to distinguish several proposed candidates of
Z2 spin liquid states on the kagome lattice.
In quantum spin liquid states, the fractionalized spinon excitations can carry fractional crystal symmetry quantum numbers, and this symmetry fractionalization distinguishes different symmetry-enriched spin liquid states with identical intrinsic topological order. In this work we propose a simple way to detect signatures of such crystal symmetry fractionalizations from the crystal symmetry representations of the ground state wave function. We demonstrate our method on projected Z[subscript 2] spin liquid wave functions on the kagome lattice, and show that it can be used to classify generic wave functions. Particularly our method can be used to distinguish several proposed candidates of Z[subscript 2] spin liquid states on the kagome lattice.