Theory of antiferromagnetic short-range order in the two-dimensional Heisenberg model

Abstract

We present a spin-rotation-invariant theory of short-range order in the square-lattice $S=1/2$ Heisenberg antiferromagnet based on the Green's-function projection technique for the dynamic spin susceptibility. By a generalized mean-field approximation and taking appropriate conditions for two vertex parameters, the static spin susceptibility, the antiferromagnetic correlation length, and the two-spin correlation functions of arbitrary range are calculated self-consistently over the whole temperature region. A good agreement with Monte Carlo results is found. The theory generalizes previous isotropic spin-wave approaches and provides an improved interpolation between the low-temperature and high-temperature behavior of the uniform static susceptibility. Comparing the theory with neutron-scattering data for the correlation length and magnetic susceptibility experiments on ${\mathrm{La}}_{2}{\mathrm{CuO}}_{4},$ a good quantitative agreement in the temperature dependences is obtained. The fit of the exchange energy yields $J=133\mathrm{meV}.$