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

Abstract

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 thermodynamiclimit properties of the two distinguished magnetic phases present in this system namely spin liquid and spin Peierls.

Metal-insulator-superconductor transition of spin-3/2 atoms on optical lattices

“…Among multi-component ultra-cold gases, high spin fermions such as spin-3/2 132 Cs, 9 Ba, 135 Ba, and 201 Hg attracted much attention due to the rich collective phenomena they can exhibit [15][16][17][18][19][20][21][22][23][24][25][26]. Spin-3/2 systems are expected to show emerging behavior due to the competing parameters, such as total spin-0 singlet and spin-2 quintet scattering lengths.…”