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

TL;DR

This paper introduces a dimer expansion approach to describe low-energy singlet excitations in the spin-1/2 Heisenberg antiferromagnet on a square lattice, revealing insights into magnon decay and excitation continua.

Contribution

A novel effective Hamiltonian is constructed to analyze singlet excitations, providing new understanding of their spectrum and interactions with magnons.

Findings

Singlet states are mostly above triplet states in energy.

Near (π,0), singlet energies are slightly lower than magnons.

Magnon decay into singlons may explain the observed excitation continuum.

Abstract

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 $(\pi,0)$.