We study the transport properties of one-dimensional (1D) interacting fermions through a barrier by numerically calculating the Kohn charge stiffness constant and the relative Drude weight. We find that the transport properties of the 1D Hubbard model are quite different from those of the 1D spinless fermion model. For example, the presence of the attractive interaction between electrons in the 1D Hubbard model actually suppresses the dc conductance, while a small repulsive interaction enhances the dc conductance. These results show that the spin degree of freedom plays an important role in the transport properties of the 1D interacting fermion systems.
We discuss how to perform the continuum limit of the
d-dimensional Hubbard model in the presence of a harmonic confining potential at zero temperature and fixed particle number. While for $d\ensuremath{\ge}3$ the system can be mapped into a noninteracting two-component Fermi gas in a harmonic trap, for
d=1 and 2 the two-body interaction is described by a Dirac $\ensuremath{\delta}$. We show that the properties of this continuum limit can be put in one-to-one correspondence with those obtained by applying the trap-size scaling formalism to the confined Hubbard model in the so called dilute regime (fixed number of particles and weak confinement). The correspondence for
d<3 has been tested, in the case of two particles with opposite spin, by comparing numerical exact-diagonalization results of the lattice system with those obtained in the continuum limit.
Motivated by recent angle-resolved photoemission spectroscopy (ARPES) experiments on doped one-dimensional (1D) cuprates, we investigate spectral properties of a 1D extended Hubbard model with both on-site repulsion
U and nearest-neighbor interaction
V, by employing bosonization analysis and the high-precision time-dependent variational principle (TDVP) calculations with large scale up to 300 sites. From state-of-the-art TDVP calculations, we find that the spectral weights of the holon-folding and
3kF branches evolve oppositely as a function of
V, and a moderate attractive
V may best fit the experimental results, hinting at the possible existence of sizable electron-phonon coupling in cuprates. From bosonization analysis, we show that this peculiar dichotomy of holon-folding and
3kF branches can be explained by a universal relation between the spectral intensity at arbitrary harmonic branches and the Luttinger parameters. We argue that the relation we establish can be used for detecting different interactions in various 1D systems.