15 research outputs found
Dynamic Density-Matrix Renormalization for the Symmetric Single Impurity Anderson Model
In this thesis we investigated, implemented, gauged, optimized, and applied a numerical approach given by the dynamic density-matrix renormalization (D-DMRG). The dynamic density-matrix renormalization is the extension of standard DMRG to the calculation of dynamic quantities. D-DMRG provides valuable numerical information on dynamic correlations by computing convolutions of the corresponding spectral densities. The dynamics at zero temperature is determined by computing the expectation values in the local propagator. This can be realized by targeting not only at the ground state and the excited state, but also at the resolvent applied to the excited state. This additional targeted state is called the correction vector. The calculation of the frequency-dependent correction vector is numerically extremely demanding due to the inversion of an almost singular non-hermitian matrix. We compared the performance of several iterative solvers for linear equation systems and managed to stabilize the inversion problem of the D-DMRG by using optimized algorithms. The main limitation of the correction vector D-DMRG is that one cannot obtain data for purely real frequencies but only for frequencies with a certain imaginary part. Hence the extraction of the behavior at purely real frequencies is one of the main problems to be solved in using the D-DMRG. We illustrated how and to which extent such data can be deconvolved to retrieve the wanted spectral densities. We discussed and compared various algorithms to achieve this extraction and presented a non-linear approach from the family of maximum entropy methods. This approach provides a continuous, positive ansatz for the wanted spectral density with the least bias (LB). Even relative abrupt changes of the spectral density can be reproduced satisfactorily. In the vicinity of singularities spurious oscillations occur. The least-bias ansatz can be made more robust towards small numerical inaccuracies and finite-size effects by including besides the entropy functional a xi-functional in the functional to be minimized. We investigated the dynamic propagator of the symmetric single impurity Anderson model by D-DMRG. The Abrikosov-Suhl resonance (ASR) was calculated to gauge the D-DMRG and to demonstrate that features at low energies can be resolved. The low energy scale of the SIAM was reproduced over two orders of magnitude. The Hubbard satellites were investigated. From the broadened D-DMRG raw data we extracted the width and the shifts from the atomic positions. By means of the LB extraction we were able to address the line shape of the satellites. It was found that the Hubbard satellites are strongly asymmetric, the peak is very pronounced and the maximum value is very high. The Hubbard model on the Bethe lattice with infinite coordination number was investigated by means of the dynamic mean-field theory (DMFT) using the D-DMRG as impurity solver. A high-resolution investigation of the electron spectra close to the metal-to-insulator transition in dynamic mean-field theory was presented. The all-numerical, consistent confirmation of a smooth transition at zero temperature is provided
Spectral Densities from Dynamic Density-Matrix Renormalization
Dynamic density-matrix renormalization provides valuable numerical
information on dynamic correlations by computing convolutions of the
corresponding spectral densities. Here we discuss and illustrate how and to
which extent such data can be deconvolved to retrieve the wanted spectral
densities. We advocate a nonlinear deconvolution scheme which minimizes the
bias in the ansatz for the spectral density. The procedure is illustrated for
the line shape and width of the Kondo peak (low energy feature) and for the
line shape of the Hubbard satellites (high energy feature) of the single
impurity Anderson model. It is found that the Hubbard satellites are strongly
asymmetric.Comment: RevTeX 4, 11 pages, 7 eps figures; published versio
Effective Spin Models for Spin-Phonon Chains by Flow Equations
We investigate the anti-adiabatic limit of an anti-ferromagnetic S=1/2
Heisenberg chain coupled to Einstein phonons. The flow equation method is used
to decouple the spin and the phonon part of the Hamiltonian. In the effective
spin model long range spin-spin interactions are generated. We determine the
phase transition from a gapless state to a gapped (dimerised) phase, which
occurs at a non-zero value of the spin-phonon coupling. In the effective phonon
sector a phonon hardening is observed.Comment: RevTeX, 6 pages, 4 eps figures; final version containing some
clarification
Electron spectra close to a metal-to-insulator transition
A high-resolution investigation of the electron spectra close to the
metal-to-insulator transition in dynamic mean-field theory is presented. An
all-numerical, consistent confirmation of a smooth transition at zero
temperature is provided. In particular, the separation of energy scales is
verified. Unexpectedly, sharp peaks at the inner Hubbard band edges occur in
the metallic regime. They are signatures of the important interaction between
single-particle excitations and collective modes.Comment: RevTeX 4, 4 pages, 4 eps figures; published versio
Generic susceptibilities of the half-filled Hubbard model in infinite dimensions
Around a metal-to-insulator transition driven by repulsive interaction (Mott
transition) the single particle excitations and the collective excitations are
equally important. Here we present results for the generic susceptibilities at
zero temperature in the half-filled Hubbard model in infinite dimensions.
Profiting from the high resolution of dynamic density-matrix renormalization at
all energies, results for the charge, spin and Cooper-pair susceptibilities in
the metallic and the insulating phase are computed. In the insulating phase, an
almost saturated local magnetic moment appears. In the metallic phase a
pronounced low-energy peak is found in the spin response.Comment: 12 pages, 12 figures; slight changes and one additional figure due to
referees' suggestion