Quantum spin-liquids represent exotic phases of matter that host emergent fractionalized excitations. The Kitaev model  is a two-dimensional model system in this context and relevant for recent experiments on putative quantum spin-liquid materials. Here, we present results for the Kitaev model coupled to a magnetic field along the $$ axis. Using infinite DMRG, we confirm three phases with vastly different transition fields depending on the sign of the Kitaev exchange : A topological phase hosting non-abelian anyons at low fields, an intermediate regime only existing for antiferromagnetic Kitaev exchange, and a field-polarized phase hosting topological magnons .
A novel time-evolution based on matrix product operators enables to obtain the dynamical spin-structure factor, which in presence of a field behaves very differently compared to what is known for the three-spin exchange  obtained within a perturbation theory approach . The magnetic field causes the flux degrees of freedom to become mobile. As a consequence the low-energy spectrum contains more structure and the gap in the dynamical spin-structure factor is reduced. Upon approaching the intermediate regime from high fields, the magnon modes reduce in frequency and simultaneously flatten. Near the transition, a broad continuum forms ranging down to
zero frequency. This phenomenology indicates, that the intermediate regime could be of exotic nature. Recent proposals [5-7] on the intermediate phase being a $U(1)$ spin-liquid will be discussed.
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