Incipient and well-developed entropy plateaus in spin-$S$ Kitaev models

We present results on the entropy and heat capacity of spin-$S$ honeycomb-lattice Kitaev models using high-temperature series expansions and thermal pure quantum state methods. We study models with anisotropic couplings $J_z=1\ge J_x=J_y$ 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 $\frac{1}{2}ln2$, independent of $S$. However, in the absence of anisotropy, there is an incipient entropy plateau at $S_{\text{max}}/2$, where $S_{\text{max}}$ is the infinite temperature entropy of the system. We discuss the possible underlying microscopic reasons for the origin and implications of these entropy plateaus.

Figure 1

(a) Honeycomb lattice with $J_x$, $J_y$, and $J_z$ bonds denoted by different colors. (b) An elementary plaquette with spins labeled 1–6.

Figure 2

Entropy of the isotropic spin-$S$ Kitaev model for various $S$ values. The limiting value of $S_{\text{max}}/2$ is indicated by the fits to the function $f\left(S\right)=ln(2S+1)/2+\sqrt{S}{(T/S)}^2$ for different $S$ values. The spin-half Monte Carlo simulation data are provided by Nasu et al. [13, 14].

Figure 3

Specific heat of the isotropic spin-$S$ Kitaev model for various $S$ values. The spin-half Monte Carlo simulation data are provided by Nasu et al. [13, 14].

Figure 4

Entropy of the anisotropic spin-1 Kitaev model.

Figure 5

Entropy of the anisotropic spin-3/2 Kitaev model.

Figure 6

Entropy of the anisotropic spin-2 Kitaev model.

Figure 7

Specific heat of the anisotropic spin-1 Kitaev model.

Figure 8

Specific heat of the anisotropic spin-3/2 Kitaev model.

Figure 9

Specific heat of the anisotropic spin-2 Kitaev model.

Figure 10

Specific heat of the anisotropic spin-$S$ Kitaev model with $J_x=J_y=0.2$ and $J_z=1$.

Figure 11

A set of closed loops on the honeycomb lattice shown by the thick gray lines that is also equivalent to a plaquette valence-bond state.