Spinon band flattening by its emergent gauge field in quantum kagome ice

Abstract

Fractional excitations provide a key to identifying sought-after topological quantum spin liquid states in realistic materials. Their single-particle dynamics already presents a challenging many-body problem on account of the coupling to their emergent gauge field. Here, we study the spinon excitations of kagome ice, realized at the $2/3$ magnetization plateau of spin ice, by combining up-to-$63$-site exact diagonalization with an analytical state graph mapping. We find a macroscopically degenerate mode in the spinon spectrum. It originates from the destructive interference due to the interaction with surrounding gauge fields, a form of many-body caging. We explicitly construct, and count, the concomitant many-body wave functions. Finally, we discuss the possible role of these flat modes in the magnetization process of kagome antiferromagnets, in particular with regard to the asymmetric termination of the kagome ice magnetisation plateau.

Figures (3)

• Figure 1: (Color online) (a) An example of kagome ice configuration. (b) A triplon excitation on a downward triangle. A triplon can hop to neighboring three downward triangles with flipping pairs of spins as indicated by ovals. (c) A spinon excitation on a downward triangle. A spinon can hop to neighboring four downward triangles. The corresponding state graph locally takes the same structure as a triangular Husimi cactus. Three successive hops of spinon around an upward triangle return all the spin configuration to the initial state, making a triangle in the state graph, as indicated by green dashed arrows.
• Figure 2: (Color online) (a) Density of states in the two-spinon sector obtained by exact diagonalization of $N_{\rm spin}=3\times N_1\times N_2$-spin system, which are well fitted with $\rho^{(2)}(\varepsilon)$ obtained from Eq. (\ref{['eq:twoDOS']}). (b) One-spinon density of states $\rho^{(1)}(\varepsilon)$ on the Husimi cactus, Eq. (\ref{['eq:oneDOS']}). (c) Magnetization process based on Eq. (\ref{['eq:MagnetizationProcess']}), taking $J_{z}=4J_{\pm}=8$, with several temperatures. The inset shows the magnetization curve around the $1/9$-plateau.
• Figure 3: (Color online) (a) A schematic figure of the procedure to construct a localized spinon flat mode. (b) The minimal localized flat mode as a superposition of 14 real space basis states.