A. Hübsch

Renormalization approach to many-particle systems

This paper presents a renormalization approach to many-particle systems. By starting from a bare Hamiltonian H=H 0 +H 1 with an unperturbed part H 0 and a perturbation H 1 , we define an effective Hamiltonian which has a band-diagonal shape with respect to the eigenbasis of H 0 . 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 A 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.

Single-particle excitations and phonon softening in the one-dimensional spinless Holstein model

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.

Renormalization of the electron-phonon interaction: a reformulation of the BCS-gap equation

Abstract.A recently developed renormalization approach is used to study the electron-phonon coupling in many-electron systems. By starting from an Hamiltonian which includes a small gauge symmetry breaking field, we directly derive a BCS-like equation for the energy gap from the renormalization approach. The effective electron-electron interaction for Cooper pairs does not contain any singularities. Furthermore, it is found that phonon-induced particle-hole excitations only contribute to the attractive electron-electron interaction if their energy difference is smaller than the phonon energy.

Coexistence of superconductivity and charge-density waves in a two-dimensional Holstein model at half-filling

On the one hand, in one dimension the coupling of electrons to phonons leads to a transition from a metallic to a Peierls distorted insulated state if the coupling exceeds a critical value. On the other hand, in two dimensions the electron-phonon interaction may also lead to the formation of Cooper pairs. In this letter, we study for two dimensions the competing influence of superconductivity and charge order (in conjunction with a lattice distortion) by means of the projector-based renormalization method (PRM). In this way, we can not only approach correlation functions of superconductivity and charge density wave but also have direct access to the order parameters. Increasing the electron-phonon interaction, we find a crossover behavior between a purely superconducting state and a charge-density wave where a well-defined parameter range of coexistence of superconductivity and lattice distortion exists.

Construction of size-consistent effective Hamiltonians for systems with arbitrary Hilbert space

Effective Hamiltonians are usually constructed by using canonical transformations or projection techniques. In contrast to this, we present a method for systems with arbitrary Hilbert space based on the introduction of cumulants. Cumulants guarantee size consistency, a property that is not always evident in other treatments. As a non-trivial example of use the derived method is applied to the strong-coupling limit of the half-filled Hubbard model on a general lattice in arbitrary spatial dimension for which the fourth-order expansion in t/U of the effective Hamiltonian is derived.

Realistic description of electron-energy-loss spectroscopy for one-dimensional Sr 2 CuO 3

We investigate the electron-energy loss spectrum of one-dimensional undoped CuO

Charge excitations in NaV 2 O 5

_{3}

Charge excitations inLiV2O5andNaV2O5: Similarities and differences

chains within an extended multi-band Hubbard model and an extended one-band Hubbard model, using the standard Lanczos algorithm. Short-range intersite Coulomb interactions are explicitly included in these models, and long-range interactions are treated in random-phase approximation. The results for the multi-band model with standard parameter values agree very well with experimental spectra of Sr

Theoretical study of charge excitations in NaV2O5 and LiV2O5

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Charge excitations inNaV2O5

CuO