arXiv subjects

G. Wellein

Publications and source records attributed to G. Wellein.

At least 19 recordsLinked to original sources

arXiv2015

Modeling and analyzing performance for highly optimized propagation steps of the lattice Boltzmann method on sparse lattices

Computational fluid dynamics (CFD) requires a vast amount of compute cycles on contemporary large-scale parallel computers. Hence, performance optimization is a pivotal activity in this field of computational science. Not only does it reduce the time to solution, but it also allows to minimize the energy consumption. In this work we study performance optimizations for an MPI-parallel lattice Boltzmann-based flow solver that uses a sparse lattice representation with indirect addressing. First we describe how this indirect addressing can be minimized in order to increase the single-core and chip-level performance. Second, the communication overhead is reduced via appropriate partitioning, but maintaining the single core performance improvements. Both optimizations allow to run the solver at an operating point with minimal energy consumption.

cs.DC↗

arXiv2014

Dot-bound and dispersive states in graphene quantum dot superlattices

We consider a square lattice configuration of circular gate-defined quantum dots in an unbiased graphene sheet and calculate the electronic, particularly spectral properties of finite albeit actual sample sized systems by means of a numerically exact kernel polynomial expansion technique. Analyzing the local density of states and the momentum resolved photoemission spectrum we find clear evidence for a series of quasi-bound states at the dots, which can be probed by optical measurements. We further analyze the interplay of the superlattice structure with dot localized modes on the electron energy dispersion. Effects of disordered dot lattices are discussed too.

cond-mat.mes-hall↗

arXiv2013

Effects of disorder and contacts on transport through graphene nanoribbons

We study the transport of charge carriers through finite graphene structures. The use of numerical exact kernel polynomial and Green function techniques allows us to treat actual sized samples beyond the Dirac-cone approximation. Particularly we investigate disordered nanoribbons, normal-conductor/graphene interfaces and normal-conductor/graphene/normal-conductor junctions with a focus on the behavior of the local density of states, single-particle spectral function, optical conductivity and conductance. We demonstrate that the contacts and bulk disorder will have a major impact on the electronic properties of graphene-based devices.

cond-mat.mes-hall↗

arXiv2011

Metal-insulator transition in the Edwards model

To understand how charge transport is affected by a background medium and vice versa we study a two-channel transport model which captures this interplay via a novel, effective fermion-boson coupling. By means of (dynamical) DMRG we prove that this model exhibits a metal-insulator transition at half-filling, where the metal typifies a repulsive Luttinger liquid and the insulator constitutes a charge density wave. The quantum phase transition point is determined consistently from the calculated photoemission spectra, the scaling of the Luttinger liquid exponent, the charge excitation gap, and the entanglement entropy.

cond-mat.str-el↗

arXiv2011

Spatiotemporal evolution of polaronic states in finite quantum systems

We study the quantum dynamics of small polaron formation and polaron transport through finite quantum structures in the framework of the one-dimensional Holstein model with site-dependent potentials and interactions. Combining Lanczos diagonalization with Chebyshev moment expansion of the time evolution operator, we determine how different initial states, representing stationary ground states or injected wave packets, after an electron-phonon interaction quench, develop in real space and time. Thereby, the full quantum nature and dynamics of electrons and phonons is preserved. We find that the decay out of the initial state sensitively depends on the energy and momentum of the incoming particle, the electron-phonon coupling strength, and the phonon frequency, whereupon bound polaron-phonon excited states may emerge in the strong-coupling regime. The tunneling of a Holstein polaron through a quantum wall/dot is generally accompanied by strong phonon number fluctuations due to phonon emission and re-absorption processes.

cond-mat.str-el↗

arXiv2008

Correlation-induced metal insulator transition in a two-channel fermion-boson model

We investigate charge transport within some background medium by means of an effective lattice model with a novel form of fermion-boson coupling. The bosons describe fluctuations of a correlated background. By analyzing groundstate and spectral properties of this transport model, we show how a metal-insulator quantum phase transition can occur for the half-filled band case. We discuss the evolution of a mass-asymmetric band structure in the insulating phase and establish connections to the Mott and Peierls transition scenarios.

cond-mat.str-el↗

arXiv2008

Localized polarons and doorway vibrons in finite quantum structures

We consider transport through finite quantum systems such as quantum barriers, wells, dots or junctions, coupled to local vibrational modes in the quantal regime. As a generic model we study the Holstein-Hubbard Hamiltonian with site-dependent potentials and interactions. Depending on the barrier height to electron-phonon coupling strength ratio and the phonon frequency we find distinct opposed behaviors: Vibration-mediated tunneling or intrinsic localization of (bi)polarons. These regimes are strongly manifested in the density correlations, mobility, and optical response calculated by exact numerical techniques.

cond-mat.str-el↗

arXiv2006

Spectral signatures of the Luttinger liquid to charge-density-wave transition

Electron- and phonon spectral functions of the one-dimensional, spinless-fermion Holstein model at half filling are calculated in the four distinct regimes of the phase diagram, corresponding to an attractive or repulsive Luttinger liquid at weak electron-phonon coupling, and a band- or polaronic insulator at strong coupling. The results obtained by means of kernel polynomial and systematic cluster approaches reveal substantially different physics in these regimes and further indicate that the size of the phonon frequency significantly affects the nature of the quantum Peierls phase transition.

cond-mat.str-el↗

arXiv2005

Optical absorption and activated transport in polaronic systems

We present exact results for the optical response in the one-dimensional Holstein model. In particular, by means of a refined kernel polynomial method, we calculate the ac and dc electrical conductivities at finite temperatures for a wide parameter range of electron phonon interaction. We analyze the deviations from the results of standard small polaron theory in the intermediate coupling regime and discuss non-adiabaticity effects in detail.

cond-mat.str-el↗

arXiv2005

Hole doped Hubbard ladders

The formation of stripes in six-leg Hubbard ladders with cylindrical boundary conditions is investigated for two different hole dopings, where the amplitude of the hole density modulation is determined in the limits of vanishing DMRG truncation errors and infinitely long ladders. The results give strong evidence that stripes exist in the ground state of these systems for strong but not for weak Hubbard couplings. The doping dependence of these findings is analysed.

cond-mat.str-el↗

arXiv2005

Optical response of many-polaron systems

Exact results for the density of states and the ac conductivity of the spinless Holstein model at finite carrier density are obtained combining Lanczos and kernel polynomial methods.

cond-mat.str-el↗

arXiv2005

Photoemission spectra of many-polaron systems

The cross over from low to high carrier densities in a many-polaron system is studied in the framework of the one-dimensional spinless Holstein model, using unbiased numerical methods. Combining a novel quantum Monte Carlo approach and exact diagonalization, accurate results for the single-particle spectrum and the electronic kinetic energy on fairly large systems are obtained. A detailed investigation of the quality of the Monte Carlo data is presented. In the physically most important adiabatic intermediate electron-phonon coupling regime, for which no analytical results are available, we observe a dissociation of polarons with increasing band filling, leading to normal metallic behavior, while for parameters favoring small polarons, no such density-driven changes occur. The present work points towards the inadequacy of single-polaron theories for a number of polaronic materials such as the manganites.

cond-mat.str-el↗

arXiv2005

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.

cond-mat.str-el↗

arXiv2004

Stripe formation in doped Hubbard ladders

We investigate the formation of stripes in $7\chunks \times 6$ Hubbard ladders with $4\chunks$ holes doped away from half filling using the density-matrix renormalization group (DMRG) method. A parallelized code allows us to keep enough density-matrix eigenstates (up to $m=8000$) and to study sufficiently large systems (with up to $7\chunks = 21$ rungs) to extrapolate the stripe amplitude to the limits of vanishing DMRG truncation error and infinitely long ladders. Our work gives strong evidence that stripes exist in the ground state for strong coupling ($U=12t$) but that the structures found in the hole density at weaker coupling ($U=3t$) are an artifact of the DMRG approach.

cond-mat.str-el↗

arXiv2004

Luttinger liquid versus charge density wave behaviour in the one-dimensional spinless fermion Holstein model

We discuss the nature of the different ground states of the half-filled Holstein model of spinless fermions in 1D. In the metallic regime we determine the renormalised effective coupling constant and the velocity of the charge excitations by a density-matrix renormalisation group (DMRG) finite-size scaling approach. At low (high) phonon frequencies the Luttinger liquid is characterised by an attractive (repulsive) effective interaction. In the charge-density wave Peierls-distorted state the charge structure factor scales to a finite value indicating long-range order.

cond-mat.str-el↗

arXiv2004

Quantum lattice dynamical effects on the single-particle excitations in 1D Mott and Peierls insulators

As a generic model describing quasi-one-dimensional Mott and Peierls insulators, we investigate the Holstein-Hubbard model for half-filled bands using numerical techniques. Combining Lanczos diagonalization with Chebyshev moment expansion we calculate exactly the photoemission and inverse photoemission spectra and use these to establish the phase diagram of the model. While polaronic features emerge only at strong electron-phonon couplings, pronounced phonon signatures, such as multi-quanta band states, can be found in the Mott insulating regime as well. In order to corroborate the Mott to Peierls transition scenario, we determine the spin and charge excitation gaps by a finite-size scaling analysis based on density-matrix renormalization group calculations.

cond-mat.str-el↗

arXiv2003

Parallelization Strategies for Density Matrix Renormalization Group Algorithms on Shared-Memory Systems

Shared-memory parallelization (SMP) strategies for density matrix renormalization group (DMRG) algorithms enable the treatment of complex systems in solid state physics. We present two different approaches by which parallelization of the standard DMRG algorithm can be accomplished in an efficient way. The methods are illustrated with DMRG calculations of the two-dimensional Hubbard model and the one-dimensional Holstein-Hubbard model on contemporary SMP architectures. The parallelized code shows good scalability up to at least eight processors and allows us to solve problems which exceed the capability of sequential DMRG calculations.

cond-mat.str-el↗

arXiv2002

Nature of the Peierls- to Mott-insulator transition in 1D

In order to clarify the physics of the crossover from a Peierls band insulator to a correlated Mott-Hubbard insulator, we analyze ground-state and spectral properties of the one-dimensional half-filled Holstein-Hubbard model using quasi-exact numerical techniques. In the adiabatic limit the transition is connected to the band to Mott insulator transition of the ionic Hubbard model. Depending on the strengths of the electron-phonon coupling and the Hubbard interaction the transition is either first order or evolves continuously across an intermediate phase with finite spin, charge, and optical excitation gaps.

cond-mat.str-el↗