The nontriviality of quantum spin liquids (QSLs) typically manifests in the nonlocal observables that signify their existence; however, this fact actually casts a shadow on detecting QSLs with experimentally accessible probes. Here, we provide a solution by unbiasedly demonstrating a dynamical signature of anyonic excitations and symmetry fractionalization in QSLs. Employing large-scale quantum Monte Carlo simulation and stochastic analytic continuation, we investigate the extended XXZ model on the kagome lattice, and find out that, across the phase transitions from Z_{2} QSLs to different symmetry breaking phases, spin spectral functions can reveal the presence and condensation of emergent anyonic spinon and vison excitations, in particular, the translational symmetry fractionalization of the latter, which can be served as the dynamical signature of the seemingly ephemeral QSLs in spectroscopic techniques such as inelastic neutron or resonance (inelastic) x-ray scatterings.

Barlowite Cu4(OH)6FBr shows three-dimensional (3D) long-range antiferromagnetism, which is fully suppressed in Cu3Zn(OH)6FBr with a kagome quantum spin liquid ground state. Here we report systematic studies on the evolution of magnetism in the Cu4−xZnx(OH)6FBr system as a function of x to bridge the two limits of Cu4(OH)6FBr (x=0) and Cu3Zn(OH)6FBr (x=1). Neutrondiffraction measurements reveal a hexagonal-to-orthorhombic structural change with decreasing temperature in the x = 0 sample. While confirming the 3D antiferromagnetic nature of low-temperature magnetism, the magnetic moments on some Cu 2+ sites on the kagome planes are found to be vanishingly small, suggesting strong frustration already exists in barlowite. Substitution of interlayer Cu 2+ with Zn 2+ with gradually increasing x completely suppresses the bulk magnetic order at around x = 0.4, but leaves a local secondary magnetic order up to x ∼ 0.8 with a slight decrease in its transition temperature. The high-temperature magnetic susceptibility and specific heat measurements further suggest that the intrinsic magnetic properties of kagome spin liquid planes may already appear from x > 0.3 samples. Our results reveal that the Cu4−xZnx(OH)6FBr may be the long-thought experimental playground for the systematic investigations of the quantum phase transition from a long-range antiferromagnet to a topologically ordered quantum spin liquid.

We define a percolation problem on the basis of spin configurations of the two-dimensional XY model. Neighboring spins belong to the same percolation cluster if their orientations differ less than a certain threshold called the conducting angle. The percolation properties of this model are studied by means of Monte Carlo simulations and a finite-size scaling analysis. Our simulations show the existence of percolation transitions when the conducting angle is varied, and we determine the transition point for several values of the XY coupling. It appears that the critical behavior of this percolation model can be well described by the standard percolation theory. The critical exponents of the percolation transitions, as determined by finite-size scaling, agree with the universality class of the two-dimensional percolation model on a uniform substrate. This holds over the whole temperature range, even in the low-temperature phase where the XY substrate is critical in the sense that it displays algebraic decay of correlations.