Numerical investigation of the excitation spectra of some two-dimensional S = ½ Heisenberg antiferromagnets

Abstract

Following a recent suggestion by Anderson (1973) that some S = ½ antiferromagnets may have a ground state with no Néel-type ordering, we set out to investigate how conventional antiferromagnetism appears in some systems while not in others. We have related the occurrence of spontaneous symmetry-breaking to the form of the excitation spectrum in the limit of large systems. Numerical investigation of the singlet and triplet excitation spectra has been carried out for clusters of the plane square and triangular lattices. The results have been used to gain information about certain qualitative features of the spectra for infinite systems by extrapolation. We have found that the continua of either the singlet or triplet excitations are not separated by a finite gap from the ground state in the case of the triangular lattice, while there is a large singlet gap for the square lattice. Hence we conclude that a Néel-type ground state is likely in the case of the square, lattice, while Anderson's spin-liquid ground state is a reasonable expectation for the triangular lattice.