A generalized effective spin-chain model is developed for studies of strongly interacting spinor gases in a one-dimensional (1D) optical lattice. The spinor gas is mapped to a system of spinless fermions and a spin chain. A generalized effective spin-chain Hamiltonian that acts on the mapped system is developed to study the static and dynamic properties of the spinor gas. This provides a computationally efficient alternative tool to study strongly interacting spinor gases in 1D lattice systems. This formalism permits the study of spinor gases with arbitrary spin and statistics, providing a generalized approach for 1D strongly interacting gases. By virtue of its simplicity, it provides an easier tool to study and gain deeper insights into the system. In combination with the model defined previously for continuum systems, a unified framework is developed. Studying the mapped system using this formalism recreates the physics of spinor gas in 1D lattice. Additionally, the time evolution of a quenched system is studied. The generalized effective spin-chain formalism has potential applications in the study of a multitude of interesting phenomena arising in lattice systems such as high-$T_c$ superconductivity and the spin-coherent and spin-incoherent Luttinger liquid regimes.

• Bose gases
• Cold gases in optical lattices
• Fermi gases
• Optical lattices & traps
• Strong interaction
• 1-dimensional spin chains
• Spin
• Adiabatic approximation
• Density matrix renormalization group
• Hubbard model
• Matrix product states
• Perturbative methods
• Second quantization
• t-J model