Low-energy Majorana states in spin liquid transitions in a three-dimensional Kitaev model

Maria Hermanns, Simon Trebst, Achim Rosch

Joji Nasu, Masafumi Udagawa, Yukitoshi Motome

A three-dimensional Kitaev model on a hyperhoneycomb lattice is investigated numerically at finite temperature. The Kitaev model is one of the solvable quantum spin models, where the ground state is given by gapped and gapless spin liquids, depending on the anisotropy of the interactions. This model can be rewritten as a free Majorana fermion system coupled with Z 2 variables. The density of states of Majorana fermions shows an excitation gap in the gapped region, while it is semimetallic in the gapless region reflecting the Dirac node. Performing the Monte Carlo simulation, we calculate the temperature dependence of the Majorana spectra. We find that the semimetallic dip is filled as temperature increases in the gapless region, but surprisingly, the spectrum develops an excitation gap in the region near the gapless-gapped boundary. Such changes of the low-energy spectrum appear sharply at the transition temperature from the spin liquid to the paramagnetic state. The results indicate that thermal fluctuations of the Z 2 fields significantly influence the low-energy state of Majorana fermions, especially in the spin liquid formation.

Joji Nasu, Toshiyuki Kaji, K. Matsuura +2 more

Christoph Berke, Simon Trebst, Ciarán Hickey

Magnetic fields can give rise to a plethora of phenomena in Kitaev spin systems, such as the formation of nontrivial spin liquids in two and three spatial dimensions. For the original honeycomb Kitaev model, it has recently been observed that the sign of the bond-directional exchange is of crucial relevance for the field-induced physics, with antiferromagnetic couplings giving rise to an intermediate spin liquid regime between the low-field gapped Kitaev spin liquid and the high-field polarized state, which is not present in the ferromagnetically coupled model. Here, by employing a Majorana mean-field approach for a magnetic field pointing along the [001] direction, we present a systematic study of field-induced spin liquid phases for a variety of two and three-dimensional lattice geometries. We find that antiferromagnetic couplings generically lead to (i) spin liquid phases that are considerably more stable in field than those for ferromagnetic couplings, and (ii) an intermediate spin liquid phase which arises from a change in the topology of the Majorana band structure. Close inspection of the mean-field parameters reveal that the intermediate phase occurs due to a field-driven sign change in an `effective' $z$-bond energy parameter. Our results clearly demonstrate the richness of the Majorana physics of the antiferromagnetic Kitaev models, in comparison to their ferromagnetic counterparts.

Brent Perreault, Johannes Knolle, Natalia Borisovna Perkins +1 more

We calculate the Raman response for the Kitaev spin model on the $\mathcal{H}\ensuremath{-}0, \mathcal{H}\ensuremath{-}1$, and $\mathcal{H}\ensuremath{-}\ensuremath{\infty}$ harmonic honeycomb lattices. We identify several quantitative features in the Raman spectrum that are characteristic of the spin liquid phase. Unlike the dynamical structure factor, which probes both the Majorana spinons and flux excitations that emerge from spin fractionalization, the Raman spectrum in the Kitaev models directly probes a density of states of pairs of fractional, dispersing Majorana spinons. As a consequence, the Raman spectrum in all these models is gapless for sufficiently isotropic couplings, with a low-energy power law that results from the Fermi lines (or points) of the dispersing Majorana spinons. We show that the polarization dependence of the Raman spectrum contains crucial information about the symmetry of the ground state. We also discuss to what extent the features of the Raman response that we find reflect generic properties of the spin liquid phase, and comment on their possible relevance to $\ensuremath{\alpha}$-, $\ensuremath{\beta}$-, and $\ensuremath{\gamma}\ensuremath{-}{\mathrm{Li}}_{2}{\mathrm{IrO}}_{3}$ compounds.

Ruben Verresen, Matthias Gohlke, Frank Pollmann +1 more