Berezinskii-Kosterlitz-Thouless Transition in two-Dimensional X X Z Easy-Plane Quantum Heisenberg Magnets

Abstract

The two-dimensional (2-d) XXZ model is described by the following Hamiltonian

$$\hat H = - \frac{1}{2}J\sum\limits_{i,d} {\left( {\hat S_i^x\hat S_{i + d}^x + \hat S_i^y\hat S_{i + d}^y + \lambda \hat S_i^z\hat S_{i + d}^z} \right),\,{{\left| {{{\hat S}_i}} \right|}^2}} = S\left( {S + 1} \right),$$

(1)

where the index i ≡ (i ₁, i ₂) runs over the sites of a square lattice and d = (±1, 0) or (0, ±1) runs over the displacements of the 4 nearest neighbors. Ferromagnetic (FM) and antiferromagnetic (AFM) systems are described by J > 0 and J < 0 respectively. An easy-plane anisotropy λ ∈ [0, 1) is present.