From one to two dimensions in quantum spin systems

TL;DR

This paper investigates how the ground state properties of a 2D quantum spin-1/2 antiferromagnetic Heisenberg model change as it approaches one-dimensionality, revealing divergences in derivatives at the 1D limit.

Contribution

It provides a detailed analysis of the derivatives of magnetization and energy with respect to anisotropy, highlighting critical behavior at the 1D limit.

Findings

Derivatives diverge at the 1D limit (θ=1).

Ground state energy shows critical behavior at the transition.

Magnetization derivatives indicate phase change.

Abstract

We study the first derivative of the staggered magnetization squared $dm^\dag(\theta)^2/d\theta$ and the second derivative $d^2e_0(\theta)/d\theta^2$ of the ground state energy per site. The parameter $\theta$ 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 $\theta=1$, where the anisotropic 2D model reduces to the 1D model.