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 wavenumbers 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 present a method for investigating the steady-state transport properties of one-dimensional correlated quantum systems. Using a procedure based on our analysis of finite-size effects in a related classical model (LC line) we show that stationary c
urrents can be obtained from transient currents in finite systems driven out of equilibrium. The non-equilibrium dynamics of correlated quantum systems is calculated using the time-evolving block decimation method. To demonstrate our method we determine the full I-V characteristic of the spinless fermion model with nearest-neighbour hopping t_H and interaction V_H using two different setups to generate currents (turning on/off a potential bias). Our numerical results agree with exact results for non-interacting fermions (V_H=0). For interacting fermions we find that in the linear regime eV << 4t_H the current I is independent from the setup and our numerical data agree with the predictions of the Luttinger liquid theory combined with the Bethe Ansatz solution. For larger potentials V the steady-state current depends on the current-generating setup and as V increases we find a negative differential conductance with one setup while the currents saturate at finite values in the other one. Both effects are due to finite renormalized bandwidths.
