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Register a new userResidual Entropy and Spin Fractionalizations in the Mixed-Spin Kitaev Model
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We investigate ground-state and finite temperature properties of the mixed-spin $(s, S)$ Kitaev model. When one of spins is half-integer and the other is integer, we introduce two kinds of local symmetries, which results in a macroscopic degeneracy in each energy level. Applying the exact diagonalization to several clusters with $(s, S)=(1/2, 1)$, we confirm the presence of this large degeneracy in the ground states, in contrast to the conventional Kitaev models. By means of the thermal pure quantum state technique, we calculate the specific heat, entropy, and spin-spin correlations in the system. We find that in the mixed-spin Kitaev model with $(s, S)=(1/2, 1)$, at least, the double peak structure appears in the specific heat and the plateau in the entropy at intermediate temperatures, indicating the existence of the spin fractionalization. Deducing the entropy in the mixed-spin system with $s, Sle 2$ systematically, we clarify that the smaller spin-$s$ is responsible for the thermodynamic properties at higher temperatures.
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We present results on entropy and heat-capacity of the spin-S honeycomb-lattice Kitaev models using high-temperature series expansions and thermal pure quantum (TPQ) state methods. We study models with anisotropic couplings $J_z=1ge J_x=J_y$ for spin values 1/2, 1, 3/2, and 2. We show that for $S>1/2$, any anisotropy leads to well developed plateaus in the entropy function at an entropy value of $frac{1}{2}ln{2}$, independent of $S$. However, in the absence of anisotropy, there is an incipient entropy plateau at $S_{max}/2$, where $S_{max}$ is the infinite temperature entropy of the system. We discuss possible underlying microscopic reasons for the origin and implications of these entropy plateaus.
Recent proposals for spin-1 Kitaev materials, such as honeycomb Ni oxides with heavy elements of Bi and Sb, have shown that these compounds naturally give rise to antiferromagnetic (AFM) Kitaev couplings. Conceptual interest in such AFM Kitaev systems has been sparked by the observation of a transition to a gapless $U(1)$ spin liquid at intermediate field strengths in the AFM spin-1/2 Kitaev model. However, all hitherto known spin-1/2 Kitaev materials exhibit ferromagnetic bond-directional exchanges. Here we discuss the physics of the spin-1 Kitaev model in a magnetic field and show, by extensive numerical analysis, that for AFM couplings it exhibits an extended gapless quantum spin liquid at intermediate field strengths. The close analogy to its spin-1/2 counterpart suggests that this gapless spin liquid is a $U(1)$ spin liquid with a neutral Fermi surface, that gives rise to enhanced thermal transport signatures.
Paramagnetic impurities in a quantum spin-liquid can result in Kondo effects with highly unusual properties. We have studied the effect of locally exchange-coupling a paramagnetic impurity with the spin-1/2 honeycomb Kitaev model in its gapless spin-liquid phase. The (impurity) scaling equations are found to be insensitive to the sign of the coupling. The weak and strong coupling fixed points are stable, with the latter corresponding to a noninteracting vacancy and an interacting, spin-1 defect for the antiferromagnetic and ferromagnetic cases respectively. The ground state in the strong coupling limit in both cases has a nontrivial topology associated with a finite Z2 flux at the impurity site. For the antiferromagnetic case, this result can be obtained straightforwardly owing to the integrability of the Kitaev model with a vacancy. The strong-coupling limit of the ferromagnetic case is however nonintegrable, and we address this problem through exact-diagonalization calculations with finite Kitaev fragments. Our exact diagonalization calculations indicate that that the weak to strong coupling transition and the topological phase transition occur rather close to each other and are possibly coincident. We also find an intriguing similarity between the magnetic response of the defect and the impurity susceptibility in the two-channel Kondo problem.
A minimal Kitaev-Gamma model has been recently investigated to understand various Kitaev systems. In the one-dimensional Kitaev-Gamma chain, an emergent SU(2)$_1$ phase and a rank-1 spin ordered phase with $O_hrightarrow D_4$ symmetry breaking were identified using non-Abelian bosonization and numerical techniques. However, puzzles near the antiferromagnetic Kitaev region with finite Gamma interaction remained unresolved. Here we focus on this parameter region and find that there are two new phases, namely, a rank-1 ordered phase with an $O_hrightarrow D_3$ symmetry breaking, and a peculiar Kitaev phase. Remarkably, the $O_hrightarrow D_3$ symmetry breaking corresponds to the classical magnetic order, but appears in a region very close to the antiferromagnetic Kitaev point where the quantum fluctuations are presumably very strong. In addition, a two-step symmetry breaking $O_hrightarrow D_{3d}rightarrow D_3$ is numerically observed as the length scale is increased: At short and intermediate length scales, the system behaves as having a rank-2 spin nematic order with $O_hrightarrow D_{3d}$ symmetry breaking; and at long distances, time reversal symmetry is further broken leading to the $O_hrightarrow D_3$ symmetry breaking. Finally, there is no numerical signature of spin orderings nor Luttinger liquid behaviors in the Kitaev phase whose nature is worth further studies.
We consider the quasi-two-dimensional pseudo-spin-1/2 Kitaev - Heisenberg model proposed for A2IrO3 (A=Li, Na) compounds. The spin-wave excitation spectrum, the sublattice magnetization, and the transition temperatures are calculated in the random phase approximation (RPA) for four different ordered phases, observed in the parameter space of the model: antiferomagnetic, stripe, ferromagnetic, and zigzag phases. The N{e}el temperature and temperature dependence of the sublattice magnetization are compared with the experimental data on Na2IrO3.
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