Quantum spin-liquids represent exotic phases of matter that host emergent fractionalized excitations. The Kitaev model [1] 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 $[111]$ axis. Using infinite DMRG, we confirm three phases with vastly different transition fields depending on the sign of the Kitaev exchange [2]: 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 [3].

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 [4] obtained within a perturbation theory approach [1]. 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.

[1] A. Kitaev, Ann. Phys. (NY) 321, 2 (2006).
[2] M. Gohlke, R. Moessner, and F. Pollmann, PRB 98 014418 (2018).
[3] P. A. McClarty, X.-Y. Dong, M. Gohlke, et al., PRB 98, 060404(R) (2018).
[4] J. Knolle, et al., PRB 92, 115127 (2015).
[5] C. Hickey, S. Trebst, Nat. Commun. 10, 530 (2019)
[6] L. Zhu, Y.-C. He, arXiv:1809.09091
[7] H.-C. Jiang et al., arXiv:1809.08247