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The study of CoNb$_2$O$_6$ sits at the confluence of simplicity andcomplexity: on one hand, the model for Ising chains -- the building blocks ofCoNb$_2$O$_6$ -- in a transverse field, can be exactly solved and, thus, servesas an archetype of quantum criticality; on the other hand, the weak but nonzerointerchain coupling adds geometric frustration to the stage, substantiallycomplicating the phase diagram. Here we utilize low-temperature specific heatand thermal conductivity measurements to study the low-lying magneticexcitations in CoNb$_2$O$_6$ and its spin-1 analogue NiNb$_2$O$_6$. The thermalconductivity is found to be suppressed around the quantum critical point, wherethe specific heat is enhanced due to gapless magnetic excitations, pointing tothe localized nature of the latter. These results highlight the predominantrole of frustration in determining the quantum critical magnetic excitations ofspin chains, which may furthermore underlie the remarkable similarities betweenthe phenomenology of these spin-1/2 and spin-1 systems.

Quantum Critical Magnetic Excitations in Spin-1/2 and Spin-1 Chain Systems