Magnon-bound-state hierarchy for the two-dimensional transverse-field Ising model in the ordered phase

In the ordered phase for an Ising ferromagnet, the magnons are attractive to form a series of bound states with the mass gaps, m₂<m₃<…. Each ratio m_2,3,…/m₁ (m₁: the single-magnon mass) is expected to be a universal constant in the vicinity of the critical point. In this paper, we devote ourselves to the (2+1)-dimensional counterpart, for which the universal hierarchical character remains unclear. We employed the exact diagonalization method, which enables us to calculate the dynamical susceptibility via the continued-fraction expansion. Thereby, we observe a variety of signals including m_2,3,4, and the spectrum is analyzed with the finite-size-scaling method to estimate the universal mass-gap ratios.