Resonating color state and emergent chromodynamics in the kagome antiferromagnet

We argue that the spin-wave breakdown in the Heisenberg kagome antiferromagnet signals an instability of the ground state and leads, through an emergent local constraint, to a quantum dynamics described by a gauge theory similar to that of chromodynamics. For integer spins, we show that the quantum fluctuations of the gauge modes select the $\sqrt{3}\times \sqrt{3}$ Néel state with an on-site moment renormalized by color resonances. We find nonmagnetic low-energy excitations that may be responsible for a deconfinement “transition” at experimentally accessible temperatures which we estimate.

Figure 1

Loop-induced low-energy dynamics within the three-coloring manifold of the kagome lattice (spin/color equivalence is shown), described as “gluon” dynamics. Right: the $q_1{\overline{q}}_1$ (“meson”) and $q_1{q}_2{q}_3$ (“baryon”) are high-energy “matter” excitations violating the local constraint.

Figure 2

Left: Double-well potential for the loop motion and quantized levels with even (solid line) and odd (dashed line) wave functions. Right: Barrier height distribution as a function of loop length in the three-coloring manifold. The curves shown are simple cosine functions.

Figure 3

Finite-size scaling of the order parameter of the $\sqrt{3}\times \sqrt{3}$ Néel state, extrapolating to a finite value (exact diagonalization and quantum Monte Carlo). Inset: total energy and fits assuming gapped (solid lines) or gapless (dashed lines) excitations.

Figure 4

Left: energy spectrum ($N=108$) showing no clear separation of scale. Right: the lowest finite-size gap follows $\Delta E/t\sim \exp (-\alpha N^{1/2})$, confirming the broken symmetry of the $\sqrt{3}\times \sqrt{3}$ Néel order.