Unconventional Pairing States in a Partially Polarized Spin-3/2 Hubbard Chain

The study of ultracold gases offers a gateway to rich and unique physical phenomena compared to those seen in solid state physics. The presence of a hyperfine spin F > 1/2, which can originate from spin-orbit coupling, in such physical systems allows for the generation of higher angular momenta Cooper pairs such as quintet or even septet pairs compared to spin-1/2 physics. In this discussion we focus on a Hubbard-like chain with a corresponding hyperfine F = 3/2 and investigate Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states, quintet states and even quartet states in momentum space using density matrix normalization group (DMRG) numerical techniques in 1-D. We tune our interaction strengths to examine such states in regimes corresponding to SU(4) symmetries, which are desireable for ultracold experiments, as well as more exotic non-SU(4) symmetries. By including the chemical potential μ and a non-zero external magnetic field h we explore the full "phase picture" of our spin-3/2 Hamiltonian in comparison to previous literature for hyperfine spin chains.