Generic Hubbard Hamiltonian for 1D Large-Spin Ultracold Fermionic Chains

A new version of the generalized Hubbard Hamiltonian is introduced here for high-spin ultracold fermions, which was used to study a spin-5/2 fermionic lattice numerically. The number of states in the energy multiplets agrees with the dimensions of low-order irreducible representations (IRs) for the symmetries expected. Furthermore, the exact diagonalization (ED) technique and the nearest-neighbor Casimir-Casimir correlations were employed to investigate numerically the quantum-phase transitions of 1D ultracold spin-3/2 fermionic lattices. With these IRs it was possible to explain the appearance of the symmetries in 1D ultracold spin-3/2 fermionic chains at quarter filling (one particle per site) and for repulsive interactions. Young’s diagrams were used to explain graphically the absence of exchange interactions for the SU(4) model. It is relevant that the generalized Hubbard Hamiltonian could be used to compute the hidden symmetries and reduce the problem complexity.