Snakes and Ladders

TL;DR

This paper maps complex spin ladder systems to a sigma model, identifies critical points and phase transitions, and discusses implications for experimental observation and RVB states.

Contribution

It provides a comprehensive phase diagram for spin ladders with various couplings, revealing new gapless phases when gapped chains are coupled.

Findings

Identification of critical curves in parameter space

Discovery of gapless phases from coupled gapped chains

Discussion of order parameters and hole behavior in RVB states

Abstract

We map spin ladders with $n_l$ legs and couplings $J'$ 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 ${J'\over J}$ 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 $J'/J$ 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.