Equal-time spin-spin and pair-field correlation functions are calculated for a two-chain Hubbard model using a density-matrix numerical renormalization group approach. At half filling, the antiferromagnetic and pair-field correlations both decay exponentially with the pair field having a much shorter correlation length. This is consistent with a gapped spin-liquid ground state. Below half filling, the antiferromagnetic correlations become incommensurate and the spin gap persists. The pair-field correlations appear to follow a power law decay which is similar to their noninteracting
U=0 behavior.
Using quantum Monte Carlo (QMC) simulations combined with Maximum Entropy analytic continuation as well as analytical methods, we examine the one- and two-particle dynamical properties of the Hubbard model on two coupled chains at small doping. The behavior of the single-particle spectral weight
A(k,ω) as a function of hopping anisotropy
t⊥/t at intermediate interaction strength is dominated by the transition from one-band behavior at large
t⊥/t to two-band behavior at small
t⊥/t, although interaction effects such as band-narrowing, a shift of spectral weight to higher energies in the unoccupied antibonding band and reflected structures due to short-range antiferromagnetic correlations are also present. A single-particle gap is resolved in the intermediate
t⊥/t Luther-Emery phase using Density Matrix Renormalization Group calculations. The dynamical spin and charge susceptibilities show features of the expected bonding-band Luttinger liquid behavior, as well as higher-energy features due to local excitations between the chains at large
t⊥/t, and evolve towards the behavior of two uncoupled chains as
t⊥/t is reduced. For the one hole, large
t⊥/t case, we make a detailed comparison between the QMC data and an approximation based on local rung states. At isotropic coupling and somewhat larger doping, we find that the dispersion of the single-particle bands is essentially unrenormalized from that of the noninteracting system, and that the spin and charge response functions have features also seen in random-phase-approximation calculations.
We study the interplay between an on-site Hubbard repulsion and quasiperiodic potential in one-dimensional fermion chains using the density matrix renormalization group. We find that, at half filling, the quasiperiodic potential can destroy the Mott gap, leading to a metallic Luttinger liquid phase between the gapped Mott insulator at strong repulsion and the localized gapless Aubry-Andr\'e insulator at strong quasiperiodic potential. Away from half filling, the metallic phase of the interacting model persists to larger critical strengths of the potential than in the noninteracting case, suggesting interaction-stabilized delocalization at finite doping. We characterize the Luttinger liquid through its charge and spin correlations, structure factors, and entanglement entropy.
We study finite-temperature transport properties of the one-dimensional Hubbard model using the density matrix renormalization group. Our aim is twofold: First, we compute both the charge- and the spin-current correlation function of the integrable model at half filling. The former decays rapidly, implying that the corresponding Drude weight is either zero or very small. Second, we calculate the optical charge conductivity ${\ensuremath{\sigma}}_{r}eg(\ensuremath{\omega})$ in the presence of small integrability-breaking next-nearest-neighbor interactions (the extended Hubbard model). The dc conductivity is finite and diverges as the temperature is decreased below the gap. Our results thus suggest that the half-filled, gapped Hubbard model is a normal charge conductor at finite temperatures. As a test bed for our numerics, we compute ${\ensuremath{\sigma}}_{r}eg(\ensuremath{\omega})$ for the integrable XXZ spin chain in its gapped phase.
We investigate a ladder system with two inequivalent legs, namely, a Hubbard chain and a one-dimensional electron gas. Analytical approximations, the density-matrix renormalization group method, and continuous-time quantum Monte Carlo simulations are used to determine ground-state properties, gaps, and spectral functions of this system at half-filling. Evidence for the existence of four different phases as a function of the Hubbard interaction and the rung hopping is presented. First, a Luttinger liquid exists at very weak interchain hopping. Second, a Kondo-Mott insulator with spin and charge gaps induced by an effective rung exchange coupling is found at moderate interchain hopping or strong Hubbard interaction. Third, a spin-gapped paramagnetic Mott insulator with incommensurate excitations and pairing of doped charges is observed at intermediate values of the rung hopping and the interaction. Fourth, the usual correlated band insulator is recovered for large rung hopping. We show that the wave numbers of the lowest single-particle excitations are different in each insulating phase. In particular, the three gapped phases exhibit markedly different spectral functions. We discuss the relevance of asymmetric two-leg ladder systems as models for atomic wires deposited on a substrate.
We have calculated the charge gap and spin gap for the two-chain Hubbard model as a function of the on-site Coulomb interaction and the interchain hopping amplitude. We used the density matrix renormalization group method and developed a method to calculate separately the gaps numerically for the symmetric and antisymmetric modes with respect to the exchange of the chain indices. We have found very different behaviors for the weak and strong interaction cases. Our calculated phase diagram is compared to the one obtained by Balents and Fisher using the weak coupling renormalization group technique.