Generalized effective spin chain Hamiltonian of strongly interacting spinor gases in optical lattice*

We develop an effective spin-chain model to study strongly interacting spinor gases in a one-dimensional lattice. Previous work (Phys. Rev. A 91, 043634, 2015; Phys. Rev. A 95, 043630, 2017) demonstrated a mapping of a continuum one-dimensional spinor gas with contact s-wave interaction, to the direct product of the wave function of a spinless Fermi gas with short-range p-wave interaction and a spin system governed by spin-parity projection operators. The mapping allowed for a generalized spin-chain model that captures the static and dynamics properties of the system. Here, the extension to lattice systems, provides a computationally efficient tool to study strongly interacting spinor gases in an optical lattice as an alternative to t-J Model and slave particle formalism. It allows us to study gases with arbitrary spin and statistics, providing a universal approach for one-dimensional strongly interacting gases. The spin-chain formalism being simple in its definition, provides an easier tool for study when compared to t-J model and slave particle formalism. Additionally, the extension provides an approach to study them in continuum or in lattice demonstrating the wide applicability of the spin-chain model. The mapped system reproduces the quasi-momentum distributions of SU(n) fermions (Nat. Phys. 10, 198–201, 2014), the ground states of the t-J model, momentum distributions and spin correlations studied for Fermi-Hubbard (Phys. Rev. B 41, 2326, 1990) and Bose-Hubbard Hamiltonian of 1D lattice gases at large on-site interaction. As an application, it also is used to study the dynamics of a quenched system, and the ground state behavior as a function of temperature for strongly-interacting spinor gases in 1D. The spin-chain Hamiltonian is useful in the study of a multitude of interesting phenomena arising in lattice systems such as high-T_c superconductivity, the spin-coherent Luttinger liquid and the spin-incoherent Luttinger liquid regimes.