Emergence of Nematic Paramagnet via Quantum Order-by-Disorder and a Pseudo-Goldstone Mode in Kitaev Magnets

The appearance of nontrivial phases in Kitaev materials exposed to an external magnetic field
has recently been studied intensively. Here, we elucidate the relation between the field-induced ground states of the classical and quantum spin models proposed for such materials, by using infinite density matrix renormalization group and linear spin wave theory. We consider an extended Kitaev model with additional off-diagonal spin exchanges, Γ and Γ'.
Focusing on the magnetic field along [111], we explain the origin of the nematic paramagnet, which breaks lattice-rotational symmetry and exists in an extended range. We show, that 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 [111]. In particular, the nematic paramagnet exhibits a characteristic pseudo-Goldstone mode which results from the lifting of a continuous degeneracy via quantum fluctuations.