Emergent <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi mathvariant="script">D</mml:mi> <mml:mrow> <mml:mn>8</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:m

Quantum integrability emerging near a quantum critical point (QCP) is manifested by an exotic excitation spectrum that is organized by the associated algebraic structure. A well-known example is the emergent ${E}_{8}$ integrability near the QCP of a transverse field Ising chain (TFIC), which was long predicted theoretically and initially proposed to be realized in the quasi-one-dimensional (q1D) quantum magnet ${\mathrm{CoNb}}_{2}{\mathrm{O}}_{6}$. However, later measurements on the spin excitation spectrum of this material revealed a series of satellite peaks in low energies that go beyond the description of the ${E}_{8}$ Lie algebra. Motivated by this experimental progress, we hereby revisit the spin excitations of ${\mathrm{CoNb}}_{2}{\mathrm{O}}_{6}$ by combining numerical calculation and analytical analysis. We show that, as effects of strong interchain fluctuations, the spectrum of the system near the 1D QCP is characterized by an emergent ${D}_{8}^{(1)}$ Lie algebra instead of the ${E}_{8}$ one. We further show that the ${D}_{8}^{(1)}$ spectrum can be realized in a broad class of interacting quantum systems. Our results advance the exploration and manipulation of integrability in quantum critical systems.