Spin-1/2 Heisenberg Antiferromagnet on the Spatially Anisotropic Kagome Lattice

We study the quasi-one-dimensional limit of the Spin-1/2 quantum antiferromagnet on the Kagome lattice, a model Hamiltonian that might be of relevance for the mineral volborthite [1,2]. The lattice is divided into antiferromagnetic spin-chains (exchange $J$) that are weakly coupled via intermediate ``dangling'' spins (exchange $J'$). Using bosonization, renormalization group methods, and current algebra techniques we determine the ground state as a function of $J'/J$. The case of a strictly one-dimensional Kagome strip is also discussed. \newline \newline [1] Z.~Hiroi, M.~Hanawa, N.~Kobayashi, M.~Nohara, Hidenori~Takagi, Y.~Kato, and M.~Takigawa, J. Phys. Soc. Japan \textbf{70}, 3377 (2001). \newline [2] F.~Bert, D.~Bono, P.~Mendels, F.~Ladieu, F.~Duc, J.-C.~Trumbe, and P.~Millet, Phys.~Rev.~Lett.~\textbf{95}, 087203 (2005).