Microscopic theory of the two-dimensional quantum antiferromagnet in a paramagnetic phase

Abstract

We have developed a consistent theory of the Heisenberg quantum antiferromagnet in the disordered phase with a short range antiferromagnetic order on the basis of the path integral for spin coherent states. We have presented the Lagrangian of the theory in a form which is explicitly invariant under rotations and found natural variables in terms of which one can construct a natural perturbation theory. The short wave spin fluctuations are similar to those in the spin wave theory and they are of the order of the parameter $1/2s$ where $s$ is the spin magnitude. The long wave spin fluctuations are governed by the nonlinear sigma model and are of the order of the the parameter 1/N, where $N$ is the number of field components. We also have shown that the short wave spin fluctuations must be evaluated accurately and the continuum limit in time of the path integral must be performed after all summation over the frequencies $ω$. In the framework of our approach we have obtained the response function for the spin fluctuations for all region of the frequency $ω$ and the wave vector ${\bf k}$ and have calculated the free energy of the system. We have also reproduced the known results for the spin correlation length in the lowest order in 1/N.