Snakes and Ladders

Abstract

We map spin ladders with $n_l$ legs and couplings $J^{\prime }$ across all rungs and $J(1\pm \gamma )$ along the legs, staggered in both directions, to a sigma model. Setting its $\theta =(2m+1)\pi$ (where it is known to be gapless), we locate the critical curves in the $\gamma$ versus $\frac{J^{\prime }}{J}$ plane at each $n_l$, and spin $S$. The phase diagram is rich and has some surprises: when two gapped chains are suitably coupled, the combination becomes gapless. With $n_l,\gamma$ and $J^{\prime }/J$ to control, the prospects for experimentally observing any one of these equivalent transitions seem bright. We discuss the order parameters and the behavior of holes in the RVB description.

RevTex file, 4 pages, 3 PS figures uuencoded, gzipped and .tar at the end of the latex file. Important extension to ferromagnetic ladders included (of potential experimental relevance). Typos corrected in formulas and figures