A higher dimensional generalization of the Kitaev spin liquid

Abstract

We construct an exactly solvable model of a four-dimensional Kitaev spin liquid. The lattice structure is orthorhombic and each unit-cell contains six sublattice degrees of freedom. We demonstrate that the Fermi surface of the model is made up of two-dimensional surfaces. Additionally, we evaluate the energy cost of creating visons using scattering theory. The positive bond-flip energy suggests that the system's ground state is flux-free, similar to the two-dimensional Kitaev honeycomb model. Our model sheds light on the realization of higher-dimensional fractionalization.

Figures (10)

• Figure 1: The dimensional evolution of spiral Kitaev models. (a) the honeycomb represented as a 2D flattened spiral (b) the 3D hyper-octagon and (c) the 4D hyper-hexagon, illustrated in three dimensions by projecting out the $\hat{n} = (1,1,1,0)$ direction. The blue-red bonds denote the alternating $xx,yy$ chain, while the green $zz$ bonds link the spirals.
• Figure 2: (a)The projected lattice structure of our 4D Kitaev spin liquid. The figure is obtained by first projecting along the $w$ direction and then projecting along the ${\bf n}= (1,1,1,0)$ direction. (b) Three fundamental plaquette operators for the 4D Kitaev spin liquid. There are 12 or 14 bonds in a fundamental loop. Emitter and Absorber specify the sign arrangement of a loop for the flux-free configuration.
• Figure 3: Three fundamental Wilson loops for the 4D Kitaev spin liquid. There are 12 or 14 bonds in a fundamental loop. Note that $W_1 W_2 = W_3$
• Figure 4: (a) The spectrum along a high symmetry momentum path $\Gamma\rightarrow M \rightarrow X \rightarrow K \rightarrow L \rightarrow \Gamma$. (b) Four of the six two-dimensional Fermi surfaces defined in \ref{['sixfs']}, projected into the first three dimensions $(k_1,k_2,k_3)$.
• Figure 5: (a) The density of state as a function of energy. At zero energy, the density of states is zero, suggesting that the dimension of the Fermi surface is lower than three. (b) Semilog plot for the DOS versus energy, with a slope that is consistent with $D(E)\propto |E|$