Effects of boundary on a kagome Ising model with magnetic-charge interaction

In frustrated Ising models on kagome and pyrochlore lattices, the system is described by conserved charge degrees of freedom [1]. Conserved charges serve as a "fractionalized" elementary excitation, which characterizes the topological nature of spin liquid state. The conserved charge description is useful to seek novel states induced by perturbations against the conventional nearest-neighbor model. For instance, it has been found that father-neighbor exchange interactions induce an interaction between the charges, which becomes a source of novel spin liquid state [2].
In this presentation, we elucidate the effect of boundary on this novel spin liquid state. The conserved nature of the charges naturally connects the bulk and boundary quantities through "Gauss’ law", thus the interplay between interactions of charges and boundary effects is expected to induce a novel physics. By using Monte Carlo simulations, we demonstrate that the spin state at the edges induce a finite bulk charge, which can be regarded as "bulk-boundary correspondence" in an Ising spin system [3].

[1] C. Castelnovo, R. Moessner, S. L. Sondhi, Nature 451, 42 (2008).
[2] T. Mizoguchi, L. D. C. Jaubert, and M. Udagawa, Phys. Rev. Lett. 119, 077207 (2017).
[3] T. Mizoguchi and Y. Hatsugai, in preparation.