The Quartet State of the Two-Dimensional Heisenberg Model with Spin 1/2 on a Square Lattice

Abstract

The low-energy properties of the two-dimensional Heisenberg model with spin-$\frac{1}{2}$ on a square lattice are investigated on the basis of the local dimer order. The lattice is divided into square blocks consisting of the quartet of spins. The spin variables and the Heisenberg Hamiltonian are expressed in terms of the low-energy quartet variables. On the basis of the Dyson-Maleev representation the spin-wave theory of the quartet state is developed. The spectrum of the lower magnon excitations consists of three degenerate modes with the energy gap $\Delta =0.17J$. The ground state energy per spin $E/N =-0.6J$. This preprint repeats in the main the previous one but it contains calculations of the basic corrections and therefore has complete character.