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.
Na5Cu3O6, a new member of one dimensional charge ordered chain cuprates, was synthesized via the azide/nitrate route by reacting NaN3, NaNO3 and CuO. According to single crystal X-ray analysis, one dimensional CuO2 chains built up from planar, edge-s
haring CuO4 squares are a dominant feature of the crystal structure. From the analysis of the Cu-O bond lengths we find that the system forms a Wigner lattice. The commensurate charge order allows to explicitly assign the valence states of either +2 or +3 to each copper atom resulting in a repetition according to Cu(2+)-Cu(3+)-Cu(2+)-Cu(2+)-Cu(3+)-Cu(2+). Following the theoretical analysis of the previously synthesized compounds Na3Cu2O4 and Na8Cu5O10, the magnetic susceptibility was expected to show a large dimer gap. Surprisingly, this is not the case. To resolve this puzzle, we show that the magnetic couplings in this compound are strongly affected by excitations across the Wigner charge gap. By including these contributions, which are distinct from conventional superexchange in Mott-insulators, we obtain a quantitative satisfying theoretical description of the magnetic susceptibility data.
We study the effects of hole doping on one-dimensional Mott insulators with orbital degrees of freedom. We describe the system in terms of a generalized t-J model. At a specific point in parameter space the model becomes integrable in analogy to the
one-band supersymmetric t-J model. We use the Bethe ansatz to derive a set of nonlinear integral equations which allow us to study the thermodynamics exactly. Moving away from this special point in parameter space we use the density-matrix renormalization group applied to transfer matrices to study the evolution of various phases of the undoped system with doping and temperature. Finally, we study a one-dimensional version of a realistic model for cubic titanates which includes the anisotropy of the orbital sector due to Hunds coupling. We find a transition from a phase with antiferromagnetically correlated spins to a phase where the spins are fully ferromagnetically polarized, a strong tendency towards phase separation at large Hunds coupling, as well as the possibility of an instability towards triplet superconductivity.
