The Kitaev model exhibits a quantum spin liquid hosting emergent fractionalized excitations.We study the Kitaev model on the honeycomb lattice coupled to a magnetic field along the [111] axis. Utilizing large scale matrix product based numerical models, we confirm three phases with transitions at different field strengths depending on the sign of the Kitaev exchange: a non-abelian topological phase at low fields, an enigmatic intermediate regime only present for antiferromagnetic Kitaev exchange, and a field-polarized phase. For the topological phase, we numerically observe the expected cubic scaling of the gap and extract the quantum dimension of the non-abelian anyons. Furthermore, we investigate dynamical signatures of the topological and the field-polarized phase using a matrix product operator based time evolution method.

We study the Kitaev-Heisenberg-Γ-Γ model that describes the magnetism in strong spin-orbit coupled honeycomb lattice Mott insulators. In strong [111] magnetic fields that bring the system into the fully polarized paramagnetic phase, we find that the spin wave bands carry nontrivial Chern numbers over large regions of the phase diagram implying the presence of chiral magnon edge states. In contrast to other topological magnon systems, the topological nontriviality of these systems results from the presence of magnon number non-conserving terms in the Hamiltonian. Since the effects of interactions are suppressed by J/h, the validity of the single particle picture is tunable making paramagnetic phases particularly suitable for the exploration of this physics. Using time dependent DMRG and interacting spin wave theory, we demonstrate the presence of the chiral edge mode and its evolution with field.

Motivated by recent experiments on α-RuCl3, we investigate a possible quantum spin liquid ground state of the honeycomb-lattice spin model with bond-dependent interactions. We consider the K − Γ model, where K and Γ represent the Kitaev and symmetric-anisotropic interactions between spin-1/2 moments on the honeycomb lattice. Using the infinite density matrix renormalization group (iDMRG), we provide compelling evidence for the existence of quantum spin liquid phases in an extended region of the phase diagram. In particular, we use transfer matrix spectra to show the evolution of two-particle excitations with well-defined two-dimensional dispersion, which is a strong signature of quantum spin liquid. These results are compared with predictions from Majorana mean-field theory and used to infer the quasiparticle excitation spectra. Further, we compute the dynamical structure factor using finite size cluster computations and show that the results resemble the scattering continuum seen in neutron scattering experiments on α-RuCl3. We discuss these results in light of recent and future experiments.

We introduce a matrix-product state based method to efficiently obtain dynamical response functions for two-dimensional microscopic Hamiltonians, which we apply to different phases of the Kitaev-Heisenberg model. We find significant broad high energy features beyond spin-wave theory even in the ordered phases proximate to spin liquids. This includes the phase with zig-zag order of the type observed in α-RuCl3, where we find high energy features like those seen in inelastic neutron scattering experiments. Our results provide an example of a natural path for proximate spin liquid features to arise at high energies above a conventionally ordered state, as the diffuse remnants of spin-wave bands intersect to yield a broad peak at the Brillouin zone center.Introduction. The interplay of strong interactions and quantum fluctuations in spin systems can give rise to new and exciting physics. A prominent example are quantum spin liquids (QSL), as fascinating as they are hard to detect: they lack local order parameters and are instead characterized in terms of emergent gauge fields. On the experimental side, spectroscopic measurements provide particularly useful insights into such systems, in particular by probing the fractionalised excitations (e.g. deconfined spinons) accompanying the gauge field. Such measurements can be related to dynamical response functions, e.g. inelastic neutron scattering to the dynamical structure factor. On the theoretical side, determining the ground state properties of such quantum spin models is already a hard problem, and it is even more challenging to understand the dynamics of local excitations.Here we present a combination of the density-matrix renormalization (DMRG) ground state method and a matrix-product states (MPS) based dynamical algorithm to obtain the response functions for generic twodimensional spin systems. With this we are able to access the dynamics of exotic phases that can occur in frustrated systems. Moreover it is also very useful for regular ordered phases where one would conventionally use large-S approximations, which in some cases cannot qualitatively explain certain high energy features 1,2 . We demonstrate our method by applying it to the currently much-studied Kitaev-Heisenberg model (KHM) model on the honeycomb lattice

The appearance of nontrivial phases in Kitaev materials exposed to an external magnetic field has recently been a subject of intensive studies. Here, we elucidate the relation between the field-induced ground states of the classical and quantum spin models proposed for such materials, by using the infinite density matrix renormalization group (iDMRG) and the linear spin wave theory (LSWT). We consider the K model, where and are off-diagonal spin exchanges on top of the dominant Kitaev interaction K. Focusing on the magnetic field along the [111] direction, we explain the origin of the nematic paramagnet, which breaks the lattice-rotational symmetry and exists in an extended window of magnetic field, in the quantum model. This phenomenon can be understood as the effect of quantum order-by-disorder in the frustrated ferromagnet with a continuous manifold of degenerate ground states discovered in the corresponding classical model. We compute the dynamical spin structure factors using a matrix operator based time evolution and compare them with the predictions from LSWT. We, thus, provide predictions for future inelastic neutron scattering experiments on Kitaev materials in an external magnetic field along the [111] direction. In particular, the nematic paramagnet exhibits a characteristic pseudo-Goldstone mode, which results from the lifting of a continuous degeneracy via quantum fluctuations.