Study of strongly interacting spinor gases in an optical lattice using a generalized effective spin chain Hamiltonian

We study one-dimensional strongly interacting spinor gases in an optical lattice by mapping it to an effective spin chain Hamiltonian. 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, this is extended to lattice systems, thereby providing 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 by virtue of its simple definition, provides an easier analysis tool compared to the t–J model and slave particle formalism. Additionally, the extension provides an approach to study them in-continuum or in-lattice, and can be easily extended to SU(n) gases, demonstrating the wide applicability of the spin-chain model. The mapped system reproduces the ground states of the t–J model, momentum distributions and spin correlations studied for Fermi-Hubbard Hamiltonian (Phys.Rev.B 41, 2326, 1990), and the dynamics of 1D lattice gases for large on-site interaction. 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.