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Eric Jeckelmann

Publications and source records attributed to Eric Jeckelmann.

At least 37 records · Page 2Linked to original sources
arXiv2014

Blind deconvolution of density-matrix renormalization-group spectra

We present a numerical method for calculating piecewise smooth spectral functions of correlated quantum systems in the thermodynamic limit from the spectra of finite systems computed using the dynamical or correction-vector density-matrix renormalization group method. The key idea is to consider this problem as a blind deconvolution with an unknown kernel which causes both a broadening and finite-size corrections of the spectrum. In practice, the method reduces to a least-square optimization under non-linear constraints which enforce the positivity and piecewise smoothness of spectral functions. The method is demonstrated on the single-particle density of states of one-dimensional paramagnetic Mott insulators represented by the half-filled Hubbard model on an open chain. Our results confirm that the density of states has a step-like shape but no square-root singularity at the spectrum onset.

cond-mat.str-el↗
arXiv2012

Local density of states of the one-dimensional spinless fermion model

We investigate the local density of states of the one-dimensional half-filled spinless fermion model with nearest-neighbor hopping t>0 and interaction V in its Luttinger liquid phase -2t < V <= 2t. The bulk density of states and the local density of states in open chains are calculated over the full band width 4t with an energy resolution <= 0.08t using the dynamical density-matrix renormalization group (DDMRG) method. We also perform DDMRG simulations with a resolution of 0.01t around the Fermi energy to reveal the power-law behaviour predicted by the Luttinger liquid theory for bulk and boundary density of states. The exponents are determined using a finite-size scaling analysis of DDMRG data for lattices with up to 3200 sites. The results agree with the exact exponents given by the Luttinger liquid theory combined with the Bethe Ansatz solution. The crossover from boundary to bulk density of states is analyzed. We have found that boundary effects can be seen in the local density of states at all energies even far away from the chain edges.

cond-mat.str-el↗
arXiv2008

Density-matrix renormalization group methods for momentum- and frequency-resolved dynamical correlation functions

Several density-matrix renormalization group methods have been proposed to compute the momentum- and frequency-resolved dynamical correlation functions of low-dimensional strongly correlated systems. The most relevant approaches are discussed in this contribution. Their applications in various studies of quasi-one-dimensional strongly correlated systems (spin chains, itinerant electron systems, electron-phonon systems) are reviewed.

cond-mat.str-el↗
arXiv2006

Exact numerical methods for electron-phonon problems

We present the basic principles of exact diagonalization and (dynamical) density-matrix renormalization-group approaches to the calculation of ground state and dynamical properties in electron-phonon systems.

cond-mat.str-el↗
arXiv2006

The spin-Peierls chain revisited

We extend previous analytical studies of the ground-state phase diagram of a one-dimensional Heisenberg spin chain coupled to optical phonons, which for increasing spin-lattice coupling undergoes a quantum phase transition from a gap-less to a gaped phase with finite lattice dimerisation. We check the analytical results against established four-block and new two-block density matrix renormalisation group (DMRG) calculations. Different finite-size scaling behaviour of the spin excitation gaps is found in the adiabatic and anti-adiabatic regimes.

cond-mat.str-el↗
arXiv2005

Optical conductivity of the one-dimensional dimerized Hubbard model at quarter filling

We investigate the optical conductivity in the Mott insulating phase of the one-dimensional extended Hubbard model with alternating hopping terms (dimerization) at quarter band filling. Optical spectra are calculated for the various parameter regimes using the dynamical density-matrix renormalization group method. The study of limiting cases allows us to explain the various structures found numerically in the optical conductivity of this model. Our calculations show that the dimerization and the nearest-neighbor repulsion determine the main features of the spectrum. The on-site repulsion plays only a secondary role. We discuss the consequences of our results for the theory of the optical conductivity in the Bechgaard salts.

cond-mat.str-el↗
arXiv2004

Comment on "Accurate ground-state phase diagram of the one-dimensional extended Hubbard model at half filling"

In PRB 68, 153101 (2003), Guoping Zhang presented density-matrix renormalization group (DMRG) results which contradict my DMRG calculations and Hirsch's quantum Monte Carlo (QMC) simulations for the charge-density-wave (CDW) phase boundary in the one-dimensional extended Hubbard model at half filling. In this Comment I show that Zhang's results are inaccurate and that his criticism of my work is groundless.

cond-mat.str-el↗
arXiv2004

Dynamical Density-Matrix Renormalization Group for the Mott--Hubbard insulator in high dimensions

We study the Hubbard model at half band-filling on a Bethe lattice with infinite coordination number in the paramagnetic insulating phase at zero temperature. We use the dynamical mean-field theory (DMFT) mapping to a single-impurity Anderson model with a bath whose properties have to be determined self-consistently. For a controlled and systematic implementation of the self-consistency scheme we use the fixed-energy (FE) approach to the DMFT. In FE-DMFT the onset and the width of the Hubbard bands are adjusted self-consistently but the energies of the bath levels are kept fixed relatively to both band edges during the calculation of self-consistent hybridization strengths between impurity and bath sites. Using the dynamical density-matrix renormalization group method (DDMRG) we calculate the density of states with a resolution ranging from 3% of the bare bandwidth $W=4t$ at high energies to 0.5% in the vicinity of the gap. The DDMRG resolution and accuracy for the density of states and the gap is superior to those obtained with other numerical methods in previous DMFT investigations. We find that the Mott gap closes at a critical coupling $U_{\rm c}/t=4.45 \pm 0.05$. At $U=4.5t$, we observe prominent shoulders near the onset of the Hubbard bands. They are the remainders of the quasi-particle resonance in the metallic phase which appears to split when the gap opens at $U_{\rm c}$.

cond-mat.str-el↗
arXiv2003

Density-matrix renormalisation group approach to quantum impurity problems

A dynamic density-matrix renormalisation group approach to the spectral properties of quantum impurity problems is presented. The method is demonstrated on the spectral density of the flat-band symmetric single-impurity Anderson model. We show that this approach provides the impurity spectral density for all frequencies and coupling strengths. In particular, Hubbard satellites at high energy can be obtained with a good resolution. The main difficulties are the necessary discretisation of the host band hybridised with the impurity and the resolution of sharp spectral features such as the Abrikosov-Suhl resonance.

cond-mat.str-el↗
arXiv2003

Reply to the Comment by Sandvik, Sengupta, and Campbell on ``Ground State Phase Diagram of a Half-Filled One-Dimensional Extended Hubbard Model''

In their Comment (see cond-mat/0301237), Sandvik, Sengupta, and Campbell present some numerical evidences to support the existence of an extended bond-order-wave (BOW) phase at couplings (U,V) weaker than a tricritical point (U_t,V_t) in the ground state phase diagram of the one-dimensional half-filled U-V Hubbard model. They claim that their results do not agree with the phase diagram proposed in my Letter (cond-mat/0204244), which shows a BOW phase for couplings stronger than the critical point only. However, I argue here that their results are not conclusive and do not refute the phase diagram described in the Letter.

cond-mat.str-el↗
arXiv2003

Fourth-Order Perturbation Theory for the Half-Filled Hubbard Model in Infinite Dimensions

We calculate the zero-temperature self-energy to fourth-order perturbation theory in the Hubbard interaction $U$ for the half-filled Hubbard model in infinite dimensions. For the Bethe lattice with bare bandwidth $W$, we compare our perturbative results for the self-energy, the single-particle density of states, and the momentum distribution to those from approximate analytical and numerical studies of the model. Results for the density of states from perturbation theory at $U/W=0.4$ agree very well with those from the Dynamical Mean-Field Theory treated with the Fixed-Energy Exact Diagonalization and with the Dynamical Density-Matrix Renormalization Group. In contrast, our results reveal the limited resolution of the Numerical Renormalization Group approach in treating the Hubbard bands. The momentum distributions from all approximate studies of the model are very similar in the regime where perturbation theory is applicable, $U/W \le 0.6$. Iterated Perturbation Theory overestimates the quasiparticle weight above such moderate interaction strengths.

cond-mat.str-el↗
arXiv2002

Ground-state phase diagram of a half-filled one-dimensional extended Hubbard model

The density-matrix renormalization group is used to study the phase diagram of the one-dimensional half-filled Hubbard model with on-site (U) and nearest-neighbor (V) repulsion, and hopping t. A critical line V_c(U) approximately equal to U/2 separates a Mott insulating phase from a charge-density-wave phase. The formation of bound charge excitations for V > 2t changes the phase transition from continuous to first order at a tricritical point U_t = 3.7t, V_t=2t. A frustrating effective antiferromagnetic spin coupling induces a bond-order-wave phase on the critical line V_c(U) for U_t < U < 7-8 t.

cond-mat.str-el↗
arXiv2002

Optical excitations in a one-dimensional Mott insulator

The density-matrix renormalization-group (DMRG) method is used to investigate optical excitations in the Mott insulating phase of a one-dimensional extended Hubbard model. The linear optical conductivity is calculated using the dynamical DMRG method and the nature of the lowest optically excited states is investigated using a symmetrized DMRG approach. The numerical calculations agree perfectly with field-theoretical predictions for a small Mott gap and analytical results for a large Mott gap obtained with a strong-coupling analysis. Is is shown that four types of optical excitations exist in this Mott insulator: pairs of unbound charge excitations, excitons, excitonic strings, and charge-density-wave (CDW) droplets. Each type of excitations dominates the low-energy optical spectrum in some region of the interaction parameter space and corresponds to distinct spectral features: a continuum starting at the Mott gap (unbound charge excitations), a single peak or several isolated peaks below the Mott gap (excitons and excitonic strings, respectively), and a continuum below the Mott gap (CDW droplets).

cond-mat.str-el↗
arXiv2002

Dynamical density-matrix renormalization-group method

I present a density-matrix renormalization-group (DMRG) method for calculating dynamical properties and excited states in low-dimensional lattice quantum many-body systems. The method is based on an exact variational principle for dynamical correlation functions and the excited states contributing to them. This dynamical DMRG is an alternate formulation of the correction vector DMRG but is both simpler and more accurate. The finite-size scaling of spectral functions is discussed and a method for analyzing the scaling of dense spectra is described. The key idea of the method is a size-dependent broadening of the spectrum.The dynamical DMRG and the finite-size scaling analysis are demonstrated on the optical conductivity of the one-dimensional Peierls-Hubbard model. Comparisons with analytical results show that the spectral functions of infinite systems can be reproduced almost exactly with these techniques. The optical conductivity of the Mott-Peierls insulator is investigated and it is shown that its spectrum is qualitatively different from the simple spectra observed in Peierls (band) insulators and one-dimensional Mott-Hubbard insulators.

cond-mat.str-el↗
arXiv2001

Application of the Density Matrix Renormalization Group in momentum space

We investigate the application of the Density Matrix Renormalization Group (DMRG) to the Hubbard model in momentum-space. We treat the one-dimensional models with dispersion relations corresponding to nearest-neighbor hopping and $1/r$ hopping and the two-dimensional model with isotropic nearest-neighbor hopping. By comparing with the exact solutions for both one-dimensional models and with exact diagonalization in two dimensions, we first investigate the convergence of the ground-state energy. We find variational convergence of the energy with the number of states kept for all models and parameter sets. In contrast to the real-space algorithm, the accuracy becomes rapidly worse with increasing interaction and is not significantly better at half filling. We compare the results for different dispersion relations at fixed interaction strength over bandwidth and find that extending the range of the hopping in one dimension has little effect, but that changing the dimensionality from one to two leads to lower accuracy at weak to moderate interaction strength. In the one-dimensional models at half-filling, we also investigate the behavior of the single-particle gap, the dispersion of spinon excitations, and the momentum distribution function. For the single-particle gap, we find that proper extrapolation in the number of states kept is important. For the spinon dispersion, we find that good agreement with the exact forms can be achieved at weak coupling if the large momentum-dependent finite-size effects are taken into account for nearest-neighbor hopping. For the momentum distribution, we compare with various weak-coupling and strong-coupling approximations and discuss the importance of finite-size effects as well as the accuracy of the DMRG.

cond-mat.str-el↗
arXiv1999

Metal-insulator transition in the one-dimensional Holstein model at half filling

We study the one-dimensional Holstein model with spin-1/2 electrons at half-filling. Ground state properties are calculated for long chains with great accuracy using the density matrix renormalization group method and extrapolated to the thermodynamic limit. We show that for small electron-phonon coupling or large phonon frequency, the insulating Peierls ground state predicted by mean-field theory is destroyed by quantum lattice fluctuations and that the system remains in a metallic phase with a non-degenerate ground state and power-law electronic and phononic correlations. When the electron-phonon coupling becomes large or the phonon frequency small, the system undergoes a transition to an insulating Peierls phase with a two-fold degenerate ground state, long-range charge-density-wave order, a dimerized lattice structure, and a gap in the electronic excitation spectrum.

cond-mat↗
arXiv1998

Dynamical properties of the one-dimensional Holstein model

The spectral weight functions and the optical conductivity of the Holstein model are studied on a one-dimensional six-site lattice with periodic boundary conditions for three different electron concentrations: a single electron, two electrons of opposite spins, and half filling. A density matrix approach is used to obtain an optimal phonon basis and to truncate the phonon Hilbert space without significant loss of accuracy. This approach allows us to calculate spectral functions for electrons dressed locally by the optimal phonons as well as for bare electrons. We obtain evidence for a smooth crossover from quasi-free electrons to an heavy itinerant small polaron (single-electron case) or bipolaron (two-electron case) as the electron-phonon coupling strength increases. At half filling we observe a crossover from a quasi-free-electron ground state to a quasi-degenerate Peierls charge-density-wave ground state for a finite electron-phonon coupling. This crossover is marked by an abrupt drop of the Drude weight which is vanishingly small in the Peierls phase.

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