Physics of the spin gap in the $S=1/2$ Heisenberg antiferromagnet on kagome

A combination of low spin and strong frustration makes the $S=1/2$ Heisenberg antiferromagnet on kagome a likely candidate for an unusual ground state and elementary excitations. Exact-diagonalization studies [1] on finite clusters point to a lack of magnetic order in the ground state and to an energy gap of order $J/20$ for $S=1$ excitations. The exact nature of the ground state and elementary excitations remains a subject of vigorous debate. Among the proposed ground states are chiral [2] and non-chiral [3] spin liquids and a valence-bond crystal (VBC) [4-5]; spin excitations range from deconfined spinons with a Bose [6] or Fermi statistics [2-3] to magnons [7]. We show that the system behaves as a collection of spinons, quasiparticles with $S=1/2$ and Fermi statistics, whose motion disturbs valence-bond order. Attraction between spinons, mediated by exchange, binds them into small, massive pairs of $S=0$ with a binding energy of $0.06 J$ [8]. The pair formation strongly suppresses the motion of individual spinons and makes the survival of the Singh-Huse VBC plausible. A spin excitation amounts to breaking up a pair into two (nearly) free spinons with $S=1$. The survival of the VBC is expected to lead to spinon confinement; however, small energy differences between various valence-bond configurations would make the confinement length large. \\[4pt] [1] Ch. Waldtmann et al., Eur. Phys. J. B \textbf{2,} 510 (1998).\\[0pt] [2] J. B. Marston and C. Zeng, J. Appl. Phys. \textbf{69,} 5962 (1991).\\[0pt] [3] M. B. Hastings, Phys. Rev. B \textbf{63,} 014413 (2000).\\[0pt] [4] P. Nikolic and T. Senthil, Phys. Rev. B \textbf{68,} 214415 (2003).\\[0pt] [5] R. R. P. Singh and D. A. Huse, Phys. Rev. B \textbf{76,} 180407 (2007).\\[0pt] [6] S. Sachdev, Phys. Rev. B \textbf{45,} 12377 (1992).\\[0pt] [7] R. R. P. Singh and D. A. Huse, arXiv:0801.2735. \\[0pt] [8] Z. Hao and O. Tchernyshyov, the subsequent talk.