Existence of Long-Range Magnetic Order in the Ground State of Two-Dimensional Spin-1/2 Heisenberg Antiferromagnets

Abstract

We give a rigorous proof of the existence of long-range antiferromagnetic order in the ground state of several two-dimensional spin-1/2 Heisenberg systems. Three types of systems are considered. The first type consists of an even number, N, of coupled square lattices with antiferromagnetic nearest-neighbor Heisenberg interactions. In this case, we prove the existence of long-range order (LRO) in the ground state for an interplane to inplane coupling ratio r in the range 0.16 ≤r ≤2.1 for N ≥4. Further, we prove that the antiferromagnetic bilayer with ferromagnetic next-nearest-neighbor (nnn) interplane couplings possesses LRO in the ground state for 0.21 ≤r < 1/4, where r is the absolute value of the ratio of the ferromagnetic and antiferromagnetic couplings. The final example consists of two antiferromagnetic spin-1/2 square lattices that are coupled via an antiferromagnetic nnn interplane coupling r. For r = 1, this system is effectively a spin-1 square lattice and has an ordered ground state. We show that LRO exists in the region 0.85 ≤r ≤1.