An exact scaling result for one dimensional interacting electronic systems

E. T. Y. Hsieh

Yupeng Wang, Fu-ke Pu

To specify the difference between the one-dimensional Kondo problem and the three-dimensional Kondo problem, we consider a model which describes the interaction between one-dimensional free electrons and a magnetic impurity. Bethe ansatz exact results and scaling analysis show that if J F > -| J B |, the Kondo screening occurs. There is no ferromagnetic Kondo screening in such a system but the long range antiferromagnetic Kondo coupling is relevant. As soon as the Coulomb interaction is introduced, the crossovers between the scaling trajectories in the parameter region J F < -| J B | and the trajectories in other parameter regions arise and ferromagnetic Kondo screening may occur.

H. Chamati

Andrzej M. Oleś, Guy Tréglia, D. Spanjaard +1 more

Exact results for the one-hole excitation spectra of the one-dimensional half-filled Hubbard Hamiltonian are presented. We consider short chains of N=2, 4, 6 atoms and introduce modified periodic boundary conditions which allow us to make a comparison between different N and to extrapolate the results up to infinite chains. By the increasing weight of the scattering states in the one-hole spectrum, we demonstrate a gradual disappearance of the free-electron (band) picture with increasing local electron-electron interaction U. The exact spectra of the N=6 chain verify the results of second-order perturbation theory for U/W1, where W is the bandwidth. The extrapolation to the infinite system, made with the finite-cell-scaling method, gives the gap which agrees rather well with the exact result for U/W>0.2. The average energies and weights of the band and scattering states obtained with this method for an infinite chain do not differ significantly from those of the N=6 chain.

Alfred Gold

We study spin-polarization effects in the one-dimensional electron gas with parabolic dispersion and a repulsive delta-function interaction potential. Using quasi-exact results for the unpolarized system and exact results for the fully polarized system we derive quasi-exact analytical results for the ground-state energy as a function of the spin polarization and the interaction strength. The spin susceptibility as a function of the interaction strength is calculated and compared with other calculations. We present results for the sound velocity of collective spin excitations and the sound velocity of collective density excitations.