Density matrix renormalization group study of dimerization of the Pariser-Parr-Pople model of polyacetilene

We apply the DMRG method to the Pariser-Parr-Pople hamiltonian and investigate the onset of dimerization. We deduce the parameters of the hopping term and the contribution of the sigma bonds from ab initio calculations on ethylene. Denoting by R_{ij} the C-C distances, we perform a variational optimization of the dimerization delta= (R_{i,i+1} - R_{i-1,i})/2 and of the average bond length R_0 for chains up to N=50 sites. The critical value of N at which the transition occurs is found to be between N=14 and N=18 for the present model. The asymptotic values for large N for R_0 and delta are given by 1.408(3) angstroms and 0.036(0) angstroms.Comment: 7 pages, Latex (RevTex) with 7 eps figures, to be published in the Journal of Chemical Physic

Influence of Coulomb distortion on polarization observables in elastic electromagnetic lepton hadron scattering at low energies

The formal expression for the most general polarization observable in elastic electromagnetic lepton hadron scattering at low energies is derived for the nonrelativistic regime. For the explicit evaluation the influence of Coulomb distortion on various polarization observables is calculated in a distorted wave Born approximation. Besides the hyperfine interaction also the spin-orbit interactions of lepton and hadron are included. For like charges the Coulomb repulsion reduces strongly the size of polarization observables compared to the plane wave Born approximation whereas for opposite charges the Coulomb attraction leads to a substantial increase of these observables for hadron lab kinetic energies below about 20 keV.Comment: 32 pages, 26 figures. Typos corrected, notation slightly changed, figures redrawn, one figure and references added. A condensed version is in press in Physical Review

The density matrix renormalization group method. Application to the PPP model of a cyclic polyene chain

The density matrix renormalization group (DMRG) method introduced by White for the study of strongly interacting electron systems is reviewed; the method is variational and considers a system of localized electrons as the union of two adjacent fragments A, B. A density matrix rho is introduced, whose eigenvectors corresponding to the largest eigenvalues are the most significant, the most probable states of A in the presence of B; these states are retained, while states corresponding to small eigenvalues of rho are neglected. It is conjectured that the decreasing behaviour of the eigenvalues is gaussian. The DMRG method is tested on the Pariser-Parr-Pople Hamiltonian of a cyclic polyene (CH)_N up to N=34. A Hilbert space of dimension 5 x 10^+18 is explored. The ground state energy is 10^-3 eV within the full CI value in the case N=18. The DMRG method compares favourably also with coupled cluster approximations. The unrestricted Hartree-Fock solution (which presents spin density waves) is briefly reviewed, and a comparison is made with the DMRG energy values. Finally, the spin-spin and density-density correlation functions are computed; the results suggest that the antiferromagnetic order of the exact solution does not extend up to large distances but exists locally. No charge density waves are present.Comment: 8 pages, RevTex, 2 figures, to be published in the Journal of Chemical Physic

Multiscale quantum-defect theory for two interacting atoms in a symmetric harmonic trap

We present a multiscale quantum-defect theory (QDT) for two identical atoms in a symmetric harmonic trap that combines the quantum-defect theory for the van der Waals interaction [B. Gao, Phys. Rev. A \textbf{64}, 010701(R) (2001)] at short distances with a quantum-defect theory for the harmonic trapping potential at large distances. The theory provides a systematic understanding of two atoms in a trap, from deeply bound molecular states and states of different partial waves, to highly excited trap states. It shows, e.g., that a strong $p$ wave pairing can lead to a lower energy state around the threshold than a $s$ wave pairing.Comment: 10 pages, 6 figure

Orthogonality relations in Quantum Tomography

Quantum estimation of the operators of a system is investigated by analyzing its Liouville space of operators. In this way it is possible to easily derive some general characterization for the sets of observables (i.e. the possible quorums) that are measured for the quantum estimation. In particular we analyze the reconstruction of operators of spin systems.Comment: 10 pages, 2 figure

Identification of the Beutler-Fano formula in eigenphase shifts and eigentime delays near a resonance

Eigenphase shifts and eigentime delays near a resonance for a system of one discrete state and two continua are shown to be functionals of the Beutler- Fano formulas using appropriate dimensionless energy units and line profile indices. Parameters responsible for the avoided crossing of eigenphase shifts and eigentime delays are identified. Similarly, parameters responsible for the eigentime delays due to a frame change are identified. With the help of new parameters, an analogy with the spin model is pursued for the S matrix and time delay matrix. The time delay matrix is shown to comprise three terms, one due to resonance, one due to a avoided crossing interaction, and one due to a frame change. It is found that the squared sum of time delays due to the avoided crossing interaction and frame change is unity.Comment: 17 pages, 3 figures, RevTe

Fano Resonance in a Quantum Wire with a Side-coupled Quantum Dot

We report a transport experiment on the Fano effect in a quantum connecting wire (QW) with a side-coupled quantum dot (QD). The Fano resonance occurs between the QD and the "T-shaped" junction in the wire, and the transport detects anti-resonance or forward scattered part of the wavefunction. While in this geometry it is more difficult to tune the shape of the resonance than in the previously reported Aharonov-Bohm-ring type interferometer, the resonance purely consists of the coherent part of transport. By utilizing this advantage, we have qualitatively explained the temperature dependence of the Fano effect by including the thermal broadening and the decoherence. We have also proven that this geometry can be a useful interferometer to measure the phase evolution of electrons at a QD.Comment: REVTEX, 6 pages including 5 figures, final versio

Unscreened Coulomb repulsion in the one dimensional electron gas

A tight binding model of electrons interacting via bare Coulomb repulsion is numerically investigated by use of the Density Matrix Renormalization Group method which we prove applicable also to very long range potentials. From the analysis of the elementary excitations, of the spin and charge correlation functions and of the momentum distribution, a picture consistent with the formation of a one dimensional "Wigner crystal" emerges, in quantitative agreement with a previous bosonization study. At finite doping, Umklapp scattering is shown to be ineffective in the presence of long range forces.Comment: RevTex, 5 pages with 8 eps figures. To be published on Phys. Rev.