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Weakly coupled Ising chains provide a condensed-matter realization ofconfinement. In these systems, kinks and antikinks bind into mesons due to anattractive interaction potential that increases linearly with the distancebetween the particles. While single mesons have been directly observed inexperiments, the role of the multiparticle continuum and bound states of mesonsin the excitation spectrum is far less clear. Using time-dependent densitymatrix renormalization group methods, we study the dynamical structure factorsof one- and two-spin operators in a transverse-field two-leg Ising ladder inthe ferromagnetic phase. The propagation of time-dependent correlations and thetwo-spin excitation spectrum reveal the existence of interchain bound states,which are absent in the one-spin dynamical structure factor. We also identifytwo-meson bound states that appear at higher energies, above the thresholds ofseveral two-meson continua.

Confinement and bound states of bound states in a transverse-field two-leg Ising ladder