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Register a new userIncipient and well-developed entropy plateaus in spin-S Kitaev models
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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.
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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.
The S=3/2 Kitaev honeycomb model (KHM) has defied an analytical as well as numerical understanding because it is not exactly soluble like its S=1/2 brethren and in contrast to other spin-S Kitaev models numerical methods are plagued by a massive pile up of low energy states. Here, we uncover the phase diagram of the S=3/2 KHM and find gapped and gapless quantum spin liquids (QSLs) generally coexisting with spin quadrupolar orders. Employing an SO(6) Majorana fermion representation of spin-3/2s, we find an exact representation of the conserved plaquette fluxes in terms of static Z$_2$ gauge fields akin to the S=1/2 KHM which enables us to treat the remaining interacting matter fermion sector in a parton mean-field theory. The latter provides an explanation for the extensive near degeneracy of low energy states in the gapless phase via the appearance of almost flat Majorana bands close to zero energy. Our parton description is in remarkable quantitative agreement with numerical simulations using the density matrix renormalization group method, and is furthermore corroborated by the addition of a single ion anisotropy which continuously connects the gapless Dirac QSL of our model with that of the S=1/2 KHM. We discuss the implications of our findings for materials realization of higher S=3/2 KHMs and the stability of the QSL phase with respect to additional interactions.
Magnetic fields can give rise to a plethora of phenomena in Kitaev spin systems, such as the formation of non-trivial 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.
I study a spin system consisting of strongly coupled dimers which are in turn weakly coupled in a plane by zigzag interactions. The model can be viewed as the strong-coupling limit of a two-dimensional zigzag chain structure typical, e.g., for the $(ac)$-planes of KCuCl_3. It is shown that the magnetization curve in this model has plateaus at 1/3 and 2/3 of the saturation magnetization, and an additional plateau at 1/2 can appear in a certain range of the model parameters; the critical fields are calculated perturbatively. It is argued that for the three-dimensional lattice structure of the KCuCl_3 family the plateaus at 1/4 and 3/4 of the saturation can be favored in a similar way, which might be relevant to the recent experiments on NH_4CuCl_3 by Shiramura et al., J. Phys. Soc. Jpn. {bf 67}, 1548 (1998).
We study the magnetization process of the $S=1$ Heisenberg model on a two-leg ladder with further neighbor spin-exchange interaction. We consider the interaction that couples up to the next-nearest neighbor rungs and find an exactly solvable regime where the ground states become product states. The next-nearest neighbor interaction tends to stabilize magnetization plateaus at multiples of 1/6. In most of the exactly solvable regime, a single magnetization curve shows two series of plateaus with different periodicities.
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