We propose an effective model called the "charge model", for the half-filled one-dimensional Hubbard and extended Hubbard models. In this model, spin-charge separation, which has been justified from an infinite on-site repulsion (U ) in the strict sense, is compatible with charge fluctuations. Our analyses based on the many-body Wannier functions succeeded in determining the optical conductivity spectra in large systems. The obtained spectra reproduce the spectra for the original models well even in the intermediate U region of U = 5-10T , with T being the nearestneighbor electron hopping energy. These results indicate that the spin-charge separation works fairly well in this intermediate U region against the usual expectation and that the charge model is an effective model that applies to actual quasi-one-dimensional materials classified as strongly correlated electron systems. N n=1 σ,σ c † n,σ c n,σ c † n+1,σ c n+1,σ .The termK(t) describes the transfer of electrons, where c † n,σ (c n,σ ) creates (annihilates) an electron of spin σ at site n, and A(t) is the dimensionless vector potential at time t. The electron-field coupling has been introduced into the transfer integral as a Peierls phase.The termV describes the Coulomb interaction, where V is the Coulomb interaction energy between neighboring sites. A periodic boundary condition is imposed in that c N +1,σ = c 1,σ
We investigate the formation of rashbon bound states and strong-coupling effects in an ultracold Fermi gas with a spherical spin-orbit interaction, H so = λ p p p · σ (where σ = (σ x , σ y , σ z ) are Pauli matrices). Extending the strong-coupling theory developed by Nozières and Schmitt-Rink (NSR) to include this spin-orbit coupling, we determine the superfluid phase transition temperature T c , as functions of the strength of a pairing interaction U s , as well as the spin-orbit coupling strength λ . Evaluating poles of the NSR particleparticle scattering matrix describing fluctuations in the Cooper channel, we clarify the region where rashbon bound states dominate the superfluid phase transition in the U s -λ phase diagram. Since the antisymmetric spin-orbit interaction H so breaks the inversion symmetry of the system, rashbon bound states naturally have, not only a spin-singlet and even-parity symmetry, but also a spin-triplet and odd-parity symmetry. Thus, our results would be also useful for the study of this parity mixing effect in the BCS-BEC crossover regime of a spinorbit coupled Fermi gas.
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