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We present experimental and theoretical evidence of novel bound stateformation in the low transverse field ordered phase of thequasi-one-dimensional Ising-like material CoNb$_2$O$_6$. High resolution singlecrystal inelastic neutron scattering measurements observe that small transversefields lead to a breakup of the spectrum into three parts, each evolving verydifferently upon increasing field. This can be naturally understood startingfrom the excitations of the ordered phase of the transverse field Ising model,domain wall quasiparticles (solitons). Here, the transverse field and astaggered off-diagonal exchange create one-soliton hopping terms with oppositesigns. We show that this leads to a rich spectrum and a special field, when thestrengths of the off-diagonal exchange and transverse field match, at whichsolitons become localized; the highest field investigated is very close to thisspecial regime. We solve this case analytically and find three two-solitoncontinua, along with three novel bound states. Perturbing away from this novellocalized limit, we find very good qualitative agreement with the experimentaldata. We also present calculations using exact diagonalization of a recentlyrefined Hamiltonian model for CoNb$_2$O$_6$ and using diagonalization of thetwo-soliton subspace, both of which provide a quantitative agreement with theobserved spectrum. The theoretical models qualitatively and quantitativelycapture a variety of non-trivial features in the observed spectrum, providinginsight into the underlying physics of bound state formation.

physical review. b./physical review. b

Excitations of quantum Ising chain CoNb2O6 in low transverse field:  quantitative description of bound states stabilized by off-diagonal exchange  and applied field