Emergence of nematic paramagnet via quantum order-by-disorder and pseudo-Goldstone modes in Kitaev magnets

Abstract

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.

Dynamics of visons and thermal Hall effect in perturbed Kitaev models

“…Linear order perturbation theory obtains a closing of the gap at values roughly consistent with exact diagonalization (ED) results [27,60] and a tensor network calculation [61]. Note, however, that a recent iDMRG study [62] predicts an increased stability of the spin liquid phase.…”

“…[60] (ED2) and Ref. [63] (ED3), from a tensor-network based approach [61] (TN) and from an iDMRG study [62].…”

Gapless quantum spin liquid in a honeycomb Γ magnet

“…Nonetheless, the Kitaev QSL is special because fluxŴ p is a conserved quantity, allowing for the identification of different flux sectors by the vison insertion 55 . Also of note is that a recent study suggests the existence of a nematicity due to the lattice rotational symmetry breaking 42 . We would like to stress that the symmetry of Γ model itself is discrete and the asymmetrical boundary condition could cause instability on the landscape of bond energy, making it hard to determine the nematicity in the thermodynamic limit.…”

“…A variational Monte Carlo simulation, on the other hand, suggests that it is a zigzag order 41 . Furthermore, a recent study proposes that it is a nematic paramagnet that spontaneously breaks the lattice rotational symmetry 42 .…”

Extended Kitaev magnetism in magnetic fields

“…This generally agrees with the numerical results for S = 1/2 and small clusters. 4,67,71,120 Having addressed the changes in the phase diagram, we now comment on a few extra insights that can be gained by calculating corrections to the classical parametrization angles. We shall see that these corrections have an interesting relation with order-by-disorder effects.…”