Quantum dynamics of charged and neutral magnetic solitons: Spin-charge separation in the one-dimensional Hubbard model

We demonstrate that the configuration interaction ~CI! approximation recaptures essential features of the exact ~Bethe-ansatz! solution to the one-dimensional ~1D! Hubbard model. As such, it provides a valuable route for describing effects that go beyond mean-field theory for strongly correlated electron systems in higher dimensions. The CI method systematically describes fluctuation and quantum tunneling corrections to the Hartree-Fock approximation ~HFA!. HFA predicts that doping a half-filled Hubbard chain leads to the appearance of charged spin polarons or charged domain-wall solitons in the antiferromagnetic background. The CI method, on the other hand, describes the quantum dynamics of these charged magnetic solitons and quantum tunneling effects between various mean-field configurations. In this paper, we test the accuracy of the CI method against the exact solution of the one-dimensional Hubbard model. We find remarkable agreement between the energy of the mobile charged bosonic domain wall ~as given by the CI method! and the exact energy of the doping hole ~as given by the Bethe ansatz! for the entire U/t range. The CI method also leads to a clear demonstration of the spin-charge separation in one dimension. Addition of one doping hole to the half-filled antiferromagnetic chain results in the appearance of two different carriers: a charged bosonic domain wall ~which carries the charge but no spin! and a neutral spin-1/2 domain wall ~which carries the spin but no charge!.