The Ising chain in a transverse field stands out as a paradigmatic example for a quantum phase transition. ${\mathrm{CoNb}}_2{\mathrm{O}}_6$ has been discussed as a material realization of this physics, but it was later realized that its magnetic exchange couplings are more complicated, taking the form of twisted Kitaev chains. Here we study a three-dimensional model for ${\mathrm{CoNb}}_2{\mathrm{O}}_6$, taking into account both Kitaev physics and frustrated interchain coupling, in applied magnetic field. Using semiclassical techniques at zero temperature, we map out the sequence of field-driven phases for arbitrary field direction; these include phases with commensurate and incommensurate interchain order. As a result of spin-orbit coupling, the phase diagram is extremely sensitive to small changes in the field angle. We compute static observables as well as magnetic excitation spectra in the various phases and connect our results to existing experimental data.

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• Frustrated magnetism
• Magnetic phase transitions
• Quantum phase transitions
• Holstein-Primakoff method
• Linear spin wave theory