We study thermalization in a one-dimensional quantum system consisting of a noninteracting fermionic chain with each site of the chain coupled to an additional bath site. Using a density matrix renormalization group algorithm we investigate the time evolution of observables in the chain after a quantum quench. For low densities we show that the intermediate time dynamics can be quantitatively described by a system of coupled equations of motion. For higher densities our numerical results show a prethermalization for local observables at intermediate times and a full thermalization to the grand canonical ensemble at long times. For the case of a weak bath-chain coupling we find, in particular, a Fermi momentum distribution in the chain in equilibrium in spite of the seemingly oversimplified bath in our model.
We investigate a model system for the injection of fermionic particles from filled source sites into an empty chain. We study the ensuing dynamics for Hermitian as well as for non-Hermitian time evolution where the particles cannot return to the bath sites (quantum ratchet). A non-homogeneous hybridization between bath and chain sites permits transient currents in the chain. Non-interacting particles show decoherence in the thermodynamic limit: the average particle number and the average current density in the chain become stationary for long times, whereas the single-particle density matrix displays large fluctuations around its mean value. Using the numerical time-dependent density-matrix renormalization group ($t$-DMRG) method we demonstrate, on the other hand, that sizable density-density interactions between the particles introduce relaxation which is by orders of magnitudes faster than the decoherence processes.
We use the density-matrix renormalization group method to investigate ground-state and dynamic properties of the one-dimensional Bose-Hubbard model, the effective model of ultracold bosonic atoms in an optical lattice. For fixed maximum site occupancy $n_b=5$, we calculate the phase boundaries between the Mott insulator and the `superfluid phase for the lowest two Mott lobes. We extract the Tomonaga-Luttinger parameter from the density-density correlation function and determine accurately the critical interaction strength for the Mott transition. For both phases, we study the momentum distribution function in the homogeneous system, and the particle distribution and quasi-momentum distribution functions in a parabolic trap. With our zero-temperature method we determine the photoemission spectra in the Mott insulator and in the `superfluid phase of the one-dimensional Bose-Hubbard model. In the insulator, the Mott gap separates the quasi-particle and quasi-hole dispersions. In the `superfluid phase the spectral weight is concentrated around zero momentum.
We use the Random Dispersion Approximation (RDA) to study the Mott-Hubbard transition in the Hubbard model at half band filling. The RDA becomes exact for the Hubbard model in infinite dimensions. We implement the RDA on finite chains and employ the Lanczos exact diagonalization method in real space to calculate the ground-state energy, the average double occupancy, the charge gap, the momentum distribution, and the quasi-particle weight. We find a satisfactory agreement with perturbative results in the weak- and strong-coupling limits. A straightforward extrapolation of the RDA data for $Lleq 14$ lattice results in a continuous Mott-Hubbard transition at $U_{rm c}approx W$. We discuss the significance of a possible signature of a coexistence region between insulating and metallic ground states in the RDA that would correspond to the scenario of a discontinuous Mott-Hubbard transition as found in numerical investigations of the Dynamical Mean-Field Theory for the Hubbard model.
We investigate the half-filled Hubbard chain with additional nearest- and next-nearest-neighbor spin exchange, J1 and J2, using bosonization and the density-matrix renormalization group. For J2 = 0 we find a spin-density-wave phase for all positive values of the Hubbard interaction U and the Heisenberg exchange J1. A frustrating spin exchange J2 induces a bond-order-wave phase. For some values of J1, J2 and U, we observe a spin-gapped metallic Luther-Emery phase.
For hopping transport in disordered materials, the mobility of charge carriers is strongly dependent on temperature and the electric field. Our numerical study shows that both the energy distribution and the mobility of charge carriers in systems with a Gaussian density of states, such as organic disordered semiconductors, can be described by a single parameter - effective temperature, dependent on the magnitude of the electric field. Furthermore, this effective temperature does not depend on the concentration of charge carriers, while the mobility does depend on the charge carrier concentration. The concept of the effective temperature is shown to be valid for systems with and without space-energy correlations in the distribution of localized states.
We use the Gutzwiller variational theory to investigate the electronic and the magnetic properties of fcc-Nickel. Our particular focus is on the effects of the spin-orbit coupling. Unlike standard relativistic band-structure theories, we reproduce the experimental magnetic moment direction and we explain the change of the Fermi-surface topology that occurs when the magnetic moment direction is rotated by an external magnetic field. The Fermi surface in our calculation deviates from early de-Haas--van-Alphen (dHvA) results. We attribute these discrepancies to an incorrect interpretation of the raw dHvA data.
