Energy Spectrum Analysis of 1D Spin-3/2 Fermionic Chains

We study an ultracold atomic gas of repulsively interacting spin-3 /2 fermions loaded into one-dimensional optical lattices. The physics of the lowest band can be described by a Hubbard Hamiltonian that becomes a generalized Heisenberg model for strong enough interactions since the system undergoes into a Mott insulator phase. For few lattice sites (up-to 6 sites), we solve numerically this model by means of the exact diagonalization technique. For larger systems (up-to 9 sites), we use the Lanczos algorithm in order to infer the physics expected in the thermodynamic limit. We present the numerical calculation of the energy spectrum and the energy gap as a function of the lattice sizes, and performing finite-size scaling we show that such small systems are able to recover the main thermodynamic-limit properties of the two distinguished magnetic phases present in this system namely spin liquid and spin Peierls.