We investigate the ground-state phase diagram of the quarter-filled Hubbard ladder with nearest-neighbor Coulomb repulsion V using the density matrix renormalization-group technique. The ground state is homogeneous at small V, a ''checkerboard'' charge-ordered insulator at large V and not too small on site Coulomb repulsion U, and is phase separated for moderate or large V and small U. The zero-temperature transition between the homogeneous and the charge-ordered phase is found to be second order. In both the homogeneous and the charge-ordered phases the existence of a spin gap mainly depends on the ratio of interchain to intrachain hopping. In the second part of the paper we construct an effective Hamiltonian for the spin degrees of freedom in the strong-coupling, charge-ordered regime that maps the system onto a frustrated spin chain. The opening of a spin gap is thus connected with spontaneous dimerization.

This paper presents a renormalization approach to many-particle systems. By starting from a bare Hamiltonian H = H0 + H1 with an unperturbed part H0 and a perturbation H1, we define an effective Hamiltonian which has a band-diagonal shape with respect to the eigenbasis of H0. This means that all transition matrix elements are suppressed which have energy differences larger than a given cutoff λ that is smaller than the cutoff Λ of the original Hamiltonian. This property resembles a recent flow equation approach on the basis of continuous unitary transformations. For demonstration of the method we discuss an exact solvable model, as well as the Anderson-lattice model where the well-known quasiparticle behavior of heavy fermions is derived.

We investigate the influence of the electron-phonon coupling in the one-dimensional spinless Holstein model at half-filling using both a recently developed projector-based renormalization method (PRM) and an refined exact diagonalization technique in combination with the kernel polynomial method. At finite phonon frequencies the system shows a metal-insulator transition accompanied by the appearance of a Peierls distorted state at a finite critical electron-phonon coupling. We analyze the opening of a gap in terms of the (inverse) photoemission spectral functions which are evaluated in both approaches. Moreover, the PRM approach reveals the softening of a phonon at the Brillouin-zone boundary which can be understood as precursor effect of the gap formation.

Motivated by recent experiments, we study the optical conductivity of DNA in its natural environment containing water molecules and counterions. Our density functional theory calculations (using Siesta) for four base pair B-DNA with order 250 surrounding water molecules suggest a thermally activated doping of the DNA by water states which generically leads to an electronic contribution to low-frequency absorption. The main contributions to the doping result from water near DNA ends, breaks, or nicks and are thus potentially associated with temporal or structural defects in the DNA.