Dimensional Crossover in Quantum Antiferromagnets

The dimensional crossover in a spin-S nearest-neighbor Heisenberg antiferromagnet is discussed as it is tuned from a two-dimensional square lattice, of lattice spacing a, towards a spin chain by varying the width $L_y$ of a semi-infinite strip $L_x\times L_y$. For integer spins and arbitrary $L_y$, and for half integer spins with $L_y/a$ an arbitrary even integer, explicit analytical expressions for the zero temperature correlation length and the spin gap are given. For half integer spins and $L_y/a$ an odd integer, it is argued that the $c=1\mathrm{}$ behavior of the SU(2${)}_1$ Wess-Zumino-Witten fixed point is squeezed out as the width $L_y\to \infty$; here c is the conformal charge. The results specialized to $S=\frac{1}{2}$ are applied to spin-ladder systems.