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

TL;DR

This paper investigates the low-energy properties of the 2D spin-1/2 Heisenberg model on a square lattice using a quartet-based approach, revealing a gapped magnon spectrum and providing detailed corrections to previous results.

Contribution

It introduces a quartet-based low-energy effective theory for the 2D Heisenberg model, including detailed calculations of corrections to prior approximations.

Findings

Magnon spectrum with three degenerate modes and a gap of 0.17J

Ground state energy per spin of -0.6J

Development of a spin-wave theory based on quartet variables

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.