From one to two dimensions in quantum spin systems

Abstract

We study the first derivative of the staggered magnetization squared $dm^†(θ)^2/dθ$ and the second derivative $d^2e_0(θ)/dθ^2$ of the ground state energy per site. The parameter $θ$ controls the anisotropy between horizontal and vertical couplings in a two-dimensional (2D) spin-1/2 antiferromagnetic Heisenberg model. It is shown, that both derivatives diverge at $θ=1$, where the anisotropic 2D model reduces to the 1D model.