Quantum Heisenberg Antiferromagnets versus Nonlinear $\sigma$ Model Without the Large S Limit

Abstract

In this letter, I develop a new topologically invariant coherent state path integral for spin systems, and apply it to the quantum Heisenberg model on a square lattice. As a result, the quantum nonlinear $\sigma$ model for arbitrary values of spin can be directly obtained. The effective coupling constant and spin wave velocity are modified by $g_s=\frac{2}{S}\sqrt{d+\frac{T_{\Lambda }}{2SJ}}$ and $c_s=2JSa\sqrt{d+\frac{T_{\Lambda }}{2SJ}}$, where $T_{\Lambda }$ is a natural temperature scale for the reliability of the theory. The formulation can also be extended to other generalized coherent state path integrals.

RevTex, 4page, no figure