  The quasi-one-dimensional (1D) Ising ferromagnet CoNb$_2$O$_6$ has recently
been driven via applied transverse magnetic fields through a continuous quantum
phase transition from spontaneous magnetic order to a quantum paramagnet, and
dramatic changes were observed in the spin dynamics, characteristic of weakly
perturbed 1D Ising quantum criticality. We report here extensive single-crystal
inelastic neutron scattering measurements of the magnetic excitations
throughout the three-dimensional (3D) Brillouin zone in the quantum
paramagnetic phase just above the critical field to characterize the effects of
the finite interchain couplings. In this phase, we observe that excitations
have a sharp, resolution-limited line shape at low energies and over most of
the dispersion bandwidth, as expected for spin-flip quasiparticles. We map the
full bandwidth along the strongly dispersive chain direction and resolve clear
modulations of the dispersions in the plane normal to the chains,
characteristic of frustrated interchain couplings in an antiferromagnetic
isosceles triangular lattice. The dispersions can be well parametrized using a
linear spin-wave model that includes interchain couplings and further neighbor
exchanges. The observed dispersion bandwidth along the chain direction is
smaller than that predicted by a linear spin-wave model using exchange values
determined at zero field, and this effect is attributed to quantum
renormalization of the dispersion beyond the spin-wave approximation in fields
slightly above the critical field, where quantum fluctuations are still
significant.
