Restoration of symmetry in the spectrum of the bilayer Heisenberg antiferromagnet

The longitudinal mode in the Heisenberg model on a bilayer square lattice is studied using series expansion methods. It is demonstrated numerically that the longitudinal mode becomes degenerate with the magnon modes at the quantum phase transition between N\'eel and dimerized phases, thus forming a spin-1 multiplet, in accord with the restoration of SU(2) symmetry. Finally, it is shown that the magnon mode becomes degenerate with the triplet mode in the dimerized phase at the critical point, showing continuity of the excitation spectrum across the critical point.