Single atomic wires of transition metal compounds have been successfully isolated within carbon nanotubes. These real one-dimensional (1D) materials with enhanced electron-electron correlations and strong electron-phonon coupling provide a unique platform to explore the competition and synergy among different quantum phases. Here we predict a new single atomic wire of niobium triiodide (${\mathrm{NbI}}_3$). Under the ${\mathrm{D}}_{2\mathrm{h}}$ symmetry, pronounced states from localized Nb-$d$ orbitals emerge at the Fermi level, inducing strong electron correlations and instability. Inclusion of Hubbard $U$ leads to a metal-to-insulator transition. Simultaneous Peierls dimerization occurs and coexists with the Mott state. Consistently, our first-principles calculations identify a ground state with ${\mathrm{C}}_{2\mathrm{v}}$ symmetry in ${\mathrm{NbI}}_3$ atomic wire and antiferromagnetic order featuring strong magnetic anisotropy. Notably, the bands near the gap remain nearly flat with narrow bandwidths irrespective of the $U$ value, indicating strongly suppressed electron kinetic energy. These results shed light in exploring correlated physics in single atomic wires and pave the way for quantum devices governed by the interplay between spin and charge orders.

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• Flat bands
• Lattice dynamics
• Magnetic anisotropy
• Peierls transition
• Spin-orbit coupling
• 1-dimensional systems
• Mott insulators
• Quantum wires
• First-principles calculations