Dynamics of Kitaev spin liquids and other two-dimensional quantum spin models

Obtaining dynamical response functions for topological phases of quantum matter is a challenging but important problem, as it encodes the characteristics of its exotic excitations. To this purpose, we introduce a matrix-product state based method for two-dimensional microscopic Hamiltonians. This is applied to the different phases of the Kitaev-Heisenberg model, where we identify characteristic dynamical features. In the ordered phases proximate to the spin liquid, we find significant broad high energy features beyond spin-wave theory, which resemble those of the Kitaev model. This establishes the concept of a proximate spin liquid, which was recently invoked in the context of inelastic neutron scattering experiments on $\alpha$-RuCl$_3$. We also discuss spectral features of other two-dimensional model magnets.