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 $D_8^{\left(1\right)}$ Lie algebra instead of the $E_8$ one. We further show that the $D_8^{\left(1\right)}$ 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.

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• Critical phenomena
• Quantum criticality
• Quantum phase transitions
• 1-dimensional spin chains
• Quantum many-body systems
• Strongly correlated systems
• Bosonization
• Exact solutions for many-body systems
• Quantum field theory (low energy)
• Spin ladders
• Tensor network methods