Low-energy singlet excitations in spin- 1/2 Heisenberg antiferromagnet on square lattice

We present an approach based on a dimer expansion which describes low-energy singlet excitations (singlons) in spin-$\frac12$ Heisenberg antiferromagnet on simple square lattice. An operator ("effective Hamiltonian") is constructed whose eigenvalues give the singlon spectrum. The "effective Hamiltonian" looks like a Hamiltonian of a spin-$\frac12$ magnet in strong external magnetic field and it has a gapped spectrum. It is found that singlet states lie above triplet ones (magnons) in the whole Brillouin zone except in the vicinity of the point $(\pi,0)$, where their energies are slightly smaller. Based on this finding, we suggest that a magnon decay is possible near $(\pi,0)$ into another magnon and a singlon which may contribute to the dip of the magnon spectrum near $(\pi,0)$ and reduce the magnon lifetime. It is pointed out that the singlon-magnon continuum may contribute to the continuum of excitations observed recently near $(\pi,0)$.