The region surrounding the excitonic insulator phase is a three-component plasma composed of elec... more The region surrounding the excitonic insulator phase is a three-component plasma composed of electrons, holes, and excitons. Due to the extended nature of the excitons, their presence influences the surrounding electrons and holes. We analyze this correlation. To this end, we calculate the density of bound electrons, the density of electrons in the correlated state, the momentum-resolved exciton density, and the momentum-resolved density of electron-hole pairs that are correlated but unbound. We find qualitative differences in the electron-hole correlations between the weak-coupling and the strong-coupling regime.
We performed an extensive numerical analysis of the Holstein model. Combining variational Lanczos... more We performed an extensive numerical analysis of the Holstein model. Combining variational Lanczos diagonalisation, density matrix renormalisation group, kernel polynomial expansion, and cluster perturbation theory techniques we solved for properties of the Holstein polaron and bipolaron problems. Numerical solution of the Holstein model means that we determined the ground-state and low-lying excited states with arbitrary precision in the thermodynamic limit for any dimension. Moreover, we calculated the spectral properties (e.g. photoemission and phonon spectra), optical response and thermal transport, as well as the dynamics of polaron formation. Our approach takes into account the full quantum dynamics of the electrons and phonons and yields unbiased results for all electron-phonon interaction strengths and phonon frequencies, but is of particular value in the intermediate-coupling regime, where perturbation theories and other analytical techniques fail.
We theoretically analyse the possibility to electrostatically confine electrons in circular quant... more We theoretically analyse the possibility to electrostatically confine electrons in circular quantum dot arrays, impressed on contacted graphene nanoribbons by top gates. Utilising exact numerical techniques, we compute the scattering efficiency of a single dot and demonstrate that for small-sized scatterers the cross-sections are dominated by quantum effects, where resonant scattering leads to a series of quasi-bound dot states. Calculating the conductance and the local density of states for quantum dot superlattices we show that the resonant carrier transport through such graphene-based nanostructures can be easily tuned by varying the gate voltage.
We examine the ground-state properties of the one-dimensional Edwards spinless fermion transport ... more We examine the ground-state properties of the one-dimensional Edwards spinless fermion transport model by means of large-scale density-matrix renormalization-group calculations. Determining the single-particle gap and the Tomonaga-Luttinger liquid parameter (K ρ) at zero temperature, we prove the existence of a metal-to-insulator quantum phase transition at one-third band filling. The insulator-established by strong correlation in the background medium-typifies a charge density wave (CDW) that is commensurate with the band filling. K ρ = 2/9 is very small at the quantum critical point, and becomes K CDW ρ = 1/9 in the infinitesimally doped three-period CDW, as predicted by the bosonization approach.
Noninteracting itinerant electrons in a solid occupy Bloch one-electron states. Phonons are colle... more Noninteracting itinerant electrons in a solid occupy Bloch one-electron states. Phonons are collective vibrational excitations of the crystal lattice. The basic electron-phonon (EP) interaction process is the absorption or emission of a phonon by the electron with a simultaneous change of the electron state. From
Lecture Notes in Computational Science and Engineering
Numerous challenges have to be mastered as applications in scientific computing are being develop... more Numerous challenges have to be mastered as applications in scientific computing are being developed for post-petascale parallel systems. While ample parallelism is usually available in the numerical problems at hand, the efficient use of supercomputer resources requires not only good scalability but also a verifiably effective use of resources on the core, the processor, and the accelerator level. Furthermore, power dissipation and energy consumption are becoming further optimization targets besides time-to-solution. Performance Engineering (PE) is the pivotal strategy for developing effective parallel code on all levels of modern architectures. In this paper we report on the development and use of low-level
Applying the (infinite) density-matrix renormalisation group technique, we explore the effect of ... more Applying the (infinite) density-matrix renormalisation group technique, we explore the effect of an explicit dimerisation on the ground-state phase diagram of the spin-1 XXZ chain with single-ion anisotropy D. We demonstrate that the Haldane phase between large-D and antiferromagnetic phases survives up to a critical dimerisation only. As a further new characteristic the dimerisation induces a direct continuous Ising quantum phase transition between the large-D and antiferromagnetic phases with central charge $$c=1/2$$ c = 1 / 2 , which terminates at a critical end-point where $$c=7/10$$ c = 7 / 10 . Calculating the critical exponents of the order parameter, neutral gap and spin–spin-correlation function, we find $$\beta =1/8$$ β = 1 / 8 (1/24), $$\nu =1$$ ν = 1 (5/9), and $$\eta =1/4$$ η = 1 / 4 (3/20), respectively, which proves the Ising (tricritical Ising) universality class in accordance with field-theoretical predictions.
We report on the influence of the lattice degrees of freedom on charge, orbital and spin correlat... more We report on the influence of the lattice degrees of freedom on charge, orbital and spin correlations in colossal magnetoresistance (CMR) manganites. For the weakly doped compounds we demonstrate that the electron-phonon coupling promotes the trapping of charge carriers, the disappearance of the orbital polaron pattern and the breakdown of ferromagnetism at the CMR transition. The role of different superexchange interactions is explored.
The following chapter reveals that science in the field of molecules, interfaces and solids has p... more The following chapter reveals that science in the field of molecules, interfaces and solids has profited substantially from the computational resources provided by the High Performance Computing Center Stuttgart and the Steinbuch Centre for Computing Karlsruhe. Because of the limited space, only one-third of the generally interesting and promising contributions could be captured in the present book. We therefore selected some broadly diversified and particularly successful projects of the currently running efforts at the centres in Karlsruhe and Stuttgart in order to demonstrate the scientific progress that can be achieved by high performance computing in chemistry, physics, material science and nanotechnology. Even a small molecular system like the Zundel cation H5O2C poses a computational challenge, if describing its nuclear motion needs a fully quantum mechanical description. This is so because the complexity grows exponentially with the number of coordinates. A break-through in ...
α-T3 quantum dots Alexander Filusch, Alan R. Bishop, Avadh Saxena, Gerhard Wellein, and Holger Fe... more α-T3 quantum dots Alexander Filusch, Alan R. Bishop, Avadh Saxena, Gerhard Wellein, and Holger Fehske ∗ Institut für Physik, Universität Greifswald, 17487 Greifswald, Germany Science, Technology and Engineering Directorate, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA Theoretical Divison, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA Department of Computer Science, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany (Dated: April 16, 2021)
We examine the ground-state properties of the one-dimensional Edwards spinless fermion transport ... more We examine the ground-state properties of the one-dimensional Edwards spinless fermion transport model by means of large-scale density-matrix renormalization-group calculations. Determining the single-particle gap and the Tomonaga-Luttinger liquid parameter (K ρ) at zero temperature, we prove the existence of a metal-to-insulator quantum phase transition at one-third band filling. The insulator-established by strong correlation in the background medium-typifies a charge density wave (CDW) that is commensurate with the band filling. K ρ = 2/9 is very small at the quantum critical point, and becomes K CDW ρ = 1/9 in the infinitesimally doped three-period CDW, as predicted by the bosonization approach.
The cross over from low to high carrier densities in a many-polaron system is studied in the fram... more 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 singleparticle 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.
We report a theoretical study of the many-body effects of electronelectron interaction on the gro... more We report a theoretical study of the many-body effects of electronelectron interaction on the ground-state and spectral properties of bilayer graphene. Using a projector-based renormalization method we show that if a finite voltage difference is applied between the graphene layers electron-hole pairs can be formed and—at very low temperatures—an excitonic instability might emerge in a bilayer graphene structure. The single-particle spectral function near the Fermi surface exhibits a prominent quasi-particle peak, different from neutral (undoped) bilayer graphene. Away from the Fermi surface, we find that states strongly interact with plasmons, thereby giving rise to a broad plasmaron peak that explains prominent features of recent angle-resolved photoemission spectroscopy data. PACS numbers: 71.10.-w, 71.38.-k, 75.47.Gk, 71.70.Ej
Paper published as part of the special topic on Synthetic Gauge Field Photonics This paper was se... more Paper published as part of the special topic on Synthetic Gauge Field Photonics This paper was selected as an Editor's Pick ARTICLES YOU MAY BE INTERESTED IN On-chip optical non-reciprocity through a synthetic Hall effect for photons APL Photonics 6, 011301 (2021);
We have performed measurements of the ir absorption of SiO 2 nanoparticles confined in an argon r... more We have performed measurements of the ir absorption of SiO 2 nanoparticles confined in an argon radiofrequency plasma discharge using a Fourier transform infrared spectrometer. By varying the gas pressure of the discharge and duty cycle of the applied radiofrequency voltage, we observed a shift of the absorption peak of SiO 2. We attributed this shift to charge-dependent absorption features of SiO 2. The charge-dependent shift has been calculated for SiO 2 particles, and from comparisons with the experiment the particle charge has been retrieved using our infrared phonon resonance shift method. With the two different approaches of changing the gas pressure and altering the duty cycle, we are able to deduce a relative change of the particle charge with pressure variations and an absolute estimate of the charge with the duty cycle.
Hardware platforms in high performance computing are constantly getting more complex to handle ev... more Hardware platforms in high performance computing are constantly getting more complex to handle even when considering multicore CPUs alone. Numerous features and configuration options in the hardware and the software environment that are relevant for performance are not even known to most application users or developers. Microbenchmarks, i.e., simple codes that fathom a particular aspect of the hardware, can help to shed light on such issues, but only if they are well understood and if the results can be reconciled with known facts or performance models. The insight gained from microbenchmarks may then be applied to real applications for performance analysis or optimization. In this paper we investigate two modern Intel x86 server CPU architectures in depth: Broadwell EP and Cascade Lake SP. We highlight relevant hardware configuration settings that can have a decisive impact on code performance and show how to properly measure on-chip and off-chip data transfer bandwidths. The new victim L3 cache of Cascade Lake and its advanced replacement policy receive due attention. Finally we use DGEMM, sparse matrix-vector multiplication, and the HPCG benchmark to make a connection to relevant application scenarios.
The symmetric sparse matrix-vector multiplication (SymmSpMV) is an important building block for m... more The symmetric sparse matrix-vector multiplication (SymmSpMV) is an important building block for many numerical linear algebra kernel operations or graph traversal applications. Parallelizing SymmSpMV on today’s multicore platforms with up to 100 cores is difficult due to the need to manage conflicting updates on the result vector. Coloring approaches can be used to solve this problem without data duplication, but existing coloring algorithms do not take load balancing and deep memory hierarchies into account, hampering scalability and full-chip performance. In this work, we propose the recursive algebraic coloring engine (RACE), a novel coloring algorithm and open-source library implementation that eliminates the shortcomings of previous coloring methods in terms of hardware efficiency and parallelization overhead. We describe the level construction, distance- k coloring, and load balancing steps in RACE, use it to parallelize SymmSpMV, and compare its performance on 31 sparse matri...
Simulating quantum transport through mesoscopic, ring-shaped graphene structures, we address vari... more Simulating quantum transport through mesoscopic, ring-shaped graphene structures, we address various quantum coherence and interference phenomena. First, a perpendicular magnetic field, penetrating the graphene ring, gives rise to Aharonov-Bohm oscillations in the conductance as a function of the magnetic flux, on top of the universal conductance fluctuations. At very high fluxes the interference gets suppressed and quantum Hall edge channels develop. Second, applying an electrostatic potential to one of the ring arms, nn nor npn-junctions can be realized with particle transmission due to normal tunneling or Klein tunneling. In the latter case the Aharonov-Bohm oscillations weaken for smooth barriers. Third, if potential disorder comes in to play, both Aharonov-Bohm and Klein tunneling effects rate down, up to the point where particle localization sets in.
Much of the recent enthusiasm directed towards topological insulators [1-13] as a new state of ma... more Much of the recent enthusiasm directed towards topological insulators [1-13] as a new state of matter is motivated by their hallmark feature of protected chiral edge states. In fermionic systems, Kramers degeneracy gives rise to these entities in the presence of time-reversal symmetry (TRS) [1-3, 14, 15]. In contrast, bosonic systems obeying TRS are generally assumed to be fundamentally precluded from supporting edge states [3, 16]. In this work, we dispel this perception and experimentally demonstrate counterpropagating chiral states at the edge of a time-reversal-symmetric photonic waveguide structure. The pivotal step in our approach is encoding the effective spin of the propagating states as a degree of freedom of the underlying waveguide lattice, such that our photonic topological insulator is characterised by a Z 2-type invariant. Our findings allow for fermionic properties to be harnessed in bosonic systems, thereby opening new avenues for topological physics in photonics as well as acoustics, mechanics and even matter waves.
We address the electronic properties of quantum dots in the two-dimensional α − 𝒯3 lattice when s... more We address the electronic properties of quantum dots in the two-dimensional α − 𝒯3 lattice when subjected to a perpendicular magnetic field. Implementing an infinite mass boundary condition, we first solve the eigenvalue problem for an isolated quantum dot in the low-energy, long-wavelength approximation where the system is described by an effective Dirac-like Hamiltonian that interpolates between the graphene (pseudospin 1/2) and Dice (pseudospin 1) limits. Results are compared to a full numerical (finite-mass) tight-binding lattice calculation. In a second step we analyse charge transport through a contacted α − 𝒯3 quantum dot in a magnetic field by calculating the local density of states and the conductance within the kernel polynomial and Landauer-Büttiker approaches. Thereby the influence of a disordered environment is discussed as well. Graphical abstract
The region surrounding the excitonic insulator phase is a three-component plasma composed of elec... more The region surrounding the excitonic insulator phase is a three-component plasma composed of electrons, holes, and excitons. Due to the extended nature of the excitons, their presence influences the surrounding electrons and holes. We analyze this correlation. To this end, we calculate the density of bound electrons, the density of electrons in the correlated state, the momentum-resolved exciton density, and the momentum-resolved density of electron-hole pairs that are correlated but unbound. We find qualitative differences in the electron-hole correlations between the weak-coupling and the strong-coupling regime.
We performed an extensive numerical analysis of the Holstein model. Combining variational Lanczos... more We performed an extensive numerical analysis of the Holstein model. Combining variational Lanczos diagonalisation, density matrix renormalisation group, kernel polynomial expansion, and cluster perturbation theory techniques we solved for properties of the Holstein polaron and bipolaron problems. Numerical solution of the Holstein model means that we determined the ground-state and low-lying excited states with arbitrary precision in the thermodynamic limit for any dimension. Moreover, we calculated the spectral properties (e.g. photoemission and phonon spectra), optical response and thermal transport, as well as the dynamics of polaron formation. Our approach takes into account the full quantum dynamics of the electrons and phonons and yields unbiased results for all electron-phonon interaction strengths and phonon frequencies, but is of particular value in the intermediate-coupling regime, where perturbation theories and other analytical techniques fail.
We theoretically analyse the possibility to electrostatically confine electrons in circular quant... more We theoretically analyse the possibility to electrostatically confine electrons in circular quantum dot arrays, impressed on contacted graphene nanoribbons by top gates. Utilising exact numerical techniques, we compute the scattering efficiency of a single dot and demonstrate that for small-sized scatterers the cross-sections are dominated by quantum effects, where resonant scattering leads to a series of quasi-bound dot states. Calculating the conductance and the local density of states for quantum dot superlattices we show that the resonant carrier transport through such graphene-based nanostructures can be easily tuned by varying the gate voltage.
We examine the ground-state properties of the one-dimensional Edwards spinless fermion transport ... more We examine the ground-state properties of the one-dimensional Edwards spinless fermion transport model by means of large-scale density-matrix renormalization-group calculations. Determining the single-particle gap and the Tomonaga-Luttinger liquid parameter (K ρ) at zero temperature, we prove the existence of a metal-to-insulator quantum phase transition at one-third band filling. The insulator-established by strong correlation in the background medium-typifies a charge density wave (CDW) that is commensurate with the band filling. K ρ = 2/9 is very small at the quantum critical point, and becomes K CDW ρ = 1/9 in the infinitesimally doped three-period CDW, as predicted by the bosonization approach.
Noninteracting itinerant electrons in a solid occupy Bloch one-electron states. Phonons are colle... more Noninteracting itinerant electrons in a solid occupy Bloch one-electron states. Phonons are collective vibrational excitations of the crystal lattice. The basic electron-phonon (EP) interaction process is the absorption or emission of a phonon by the electron with a simultaneous change of the electron state. From
Lecture Notes in Computational Science and Engineering
Numerous challenges have to be mastered as applications in scientific computing are being develop... more Numerous challenges have to be mastered as applications in scientific computing are being developed for post-petascale parallel systems. While ample parallelism is usually available in the numerical problems at hand, the efficient use of supercomputer resources requires not only good scalability but also a verifiably effective use of resources on the core, the processor, and the accelerator level. Furthermore, power dissipation and energy consumption are becoming further optimization targets besides time-to-solution. Performance Engineering (PE) is the pivotal strategy for developing effective parallel code on all levels of modern architectures. In this paper we report on the development and use of low-level
Applying the (infinite) density-matrix renormalisation group technique, we explore the effect of ... more Applying the (infinite) density-matrix renormalisation group technique, we explore the effect of an explicit dimerisation on the ground-state phase diagram of the spin-1 XXZ chain with single-ion anisotropy D. We demonstrate that the Haldane phase between large-D and antiferromagnetic phases survives up to a critical dimerisation only. As a further new characteristic the dimerisation induces a direct continuous Ising quantum phase transition between the large-D and antiferromagnetic phases with central charge $$c=1/2$$ c = 1 / 2 , which terminates at a critical end-point where $$c=7/10$$ c = 7 / 10 . Calculating the critical exponents of the order parameter, neutral gap and spin–spin-correlation function, we find $$\beta =1/8$$ β = 1 / 8 (1/24), $$\nu =1$$ ν = 1 (5/9), and $$\eta =1/4$$ η = 1 / 4 (3/20), respectively, which proves the Ising (tricritical Ising) universality class in accordance with field-theoretical predictions.
We report on the influence of the lattice degrees of freedom on charge, orbital and spin correlat... more We report on the influence of the lattice degrees of freedom on charge, orbital and spin correlations in colossal magnetoresistance (CMR) manganites. For the weakly doped compounds we demonstrate that the electron-phonon coupling promotes the trapping of charge carriers, the disappearance of the orbital polaron pattern and the breakdown of ferromagnetism at the CMR transition. The role of different superexchange interactions is explored.
The following chapter reveals that science in the field of molecules, interfaces and solids has p... more The following chapter reveals that science in the field of molecules, interfaces and solids has profited substantially from the computational resources provided by the High Performance Computing Center Stuttgart and the Steinbuch Centre for Computing Karlsruhe. Because of the limited space, only one-third of the generally interesting and promising contributions could be captured in the present book. We therefore selected some broadly diversified and particularly successful projects of the currently running efforts at the centres in Karlsruhe and Stuttgart in order to demonstrate the scientific progress that can be achieved by high performance computing in chemistry, physics, material science and nanotechnology. Even a small molecular system like the Zundel cation H5O2C poses a computational challenge, if describing its nuclear motion needs a fully quantum mechanical description. This is so because the complexity grows exponentially with the number of coordinates. A break-through in ...
α-T3 quantum dots Alexander Filusch, Alan R. Bishop, Avadh Saxena, Gerhard Wellein, and Holger Fe... more α-T3 quantum dots Alexander Filusch, Alan R. Bishop, Avadh Saxena, Gerhard Wellein, and Holger Fehske ∗ Institut für Physik, Universität Greifswald, 17487 Greifswald, Germany Science, Technology and Engineering Directorate, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA Theoretical Divison, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA Department of Computer Science, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany (Dated: April 16, 2021)
We examine the ground-state properties of the one-dimensional Edwards spinless fermion transport ... more We examine the ground-state properties of the one-dimensional Edwards spinless fermion transport model by means of large-scale density-matrix renormalization-group calculations. Determining the single-particle gap and the Tomonaga-Luttinger liquid parameter (K ρ) at zero temperature, we prove the existence of a metal-to-insulator quantum phase transition at one-third band filling. The insulator-established by strong correlation in the background medium-typifies a charge density wave (CDW) that is commensurate with the band filling. K ρ = 2/9 is very small at the quantum critical point, and becomes K CDW ρ = 1/9 in the infinitesimally doped three-period CDW, as predicted by the bosonization approach.
The cross over from low to high carrier densities in a many-polaron system is studied in the fram... more 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 singleparticle 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.
We report a theoretical study of the many-body effects of electronelectron interaction on the gro... more We report a theoretical study of the many-body effects of electronelectron interaction on the ground-state and spectral properties of bilayer graphene. Using a projector-based renormalization method we show that if a finite voltage difference is applied between the graphene layers electron-hole pairs can be formed and—at very low temperatures—an excitonic instability might emerge in a bilayer graphene structure. The single-particle spectral function near the Fermi surface exhibits a prominent quasi-particle peak, different from neutral (undoped) bilayer graphene. Away from the Fermi surface, we find that states strongly interact with plasmons, thereby giving rise to a broad plasmaron peak that explains prominent features of recent angle-resolved photoemission spectroscopy data. PACS numbers: 71.10.-w, 71.38.-k, 75.47.Gk, 71.70.Ej
Paper published as part of the special topic on Synthetic Gauge Field Photonics This paper was se... more Paper published as part of the special topic on Synthetic Gauge Field Photonics This paper was selected as an Editor's Pick ARTICLES YOU MAY BE INTERESTED IN On-chip optical non-reciprocity through a synthetic Hall effect for photons APL Photonics 6, 011301 (2021);
We have performed measurements of the ir absorption of SiO 2 nanoparticles confined in an argon r... more We have performed measurements of the ir absorption of SiO 2 nanoparticles confined in an argon radiofrequency plasma discharge using a Fourier transform infrared spectrometer. By varying the gas pressure of the discharge and duty cycle of the applied radiofrequency voltage, we observed a shift of the absorption peak of SiO 2. We attributed this shift to charge-dependent absorption features of SiO 2. The charge-dependent shift has been calculated for SiO 2 particles, and from comparisons with the experiment the particle charge has been retrieved using our infrared phonon resonance shift method. With the two different approaches of changing the gas pressure and altering the duty cycle, we are able to deduce a relative change of the particle charge with pressure variations and an absolute estimate of the charge with the duty cycle.
Hardware platforms in high performance computing are constantly getting more complex to handle ev... more Hardware platforms in high performance computing are constantly getting more complex to handle even when considering multicore CPUs alone. Numerous features and configuration options in the hardware and the software environment that are relevant for performance are not even known to most application users or developers. Microbenchmarks, i.e., simple codes that fathom a particular aspect of the hardware, can help to shed light on such issues, but only if they are well understood and if the results can be reconciled with known facts or performance models. The insight gained from microbenchmarks may then be applied to real applications for performance analysis or optimization. In this paper we investigate two modern Intel x86 server CPU architectures in depth: Broadwell EP and Cascade Lake SP. We highlight relevant hardware configuration settings that can have a decisive impact on code performance and show how to properly measure on-chip and off-chip data transfer bandwidths. The new victim L3 cache of Cascade Lake and its advanced replacement policy receive due attention. Finally we use DGEMM, sparse matrix-vector multiplication, and the HPCG benchmark to make a connection to relevant application scenarios.
The symmetric sparse matrix-vector multiplication (SymmSpMV) is an important building block for m... more The symmetric sparse matrix-vector multiplication (SymmSpMV) is an important building block for many numerical linear algebra kernel operations or graph traversal applications. Parallelizing SymmSpMV on today’s multicore platforms with up to 100 cores is difficult due to the need to manage conflicting updates on the result vector. Coloring approaches can be used to solve this problem without data duplication, but existing coloring algorithms do not take load balancing and deep memory hierarchies into account, hampering scalability and full-chip performance. In this work, we propose the recursive algebraic coloring engine (RACE), a novel coloring algorithm and open-source library implementation that eliminates the shortcomings of previous coloring methods in terms of hardware efficiency and parallelization overhead. We describe the level construction, distance- k coloring, and load balancing steps in RACE, use it to parallelize SymmSpMV, and compare its performance on 31 sparse matri...
Simulating quantum transport through mesoscopic, ring-shaped graphene structures, we address vari... more Simulating quantum transport through mesoscopic, ring-shaped graphene structures, we address various quantum coherence and interference phenomena. First, a perpendicular magnetic field, penetrating the graphene ring, gives rise to Aharonov-Bohm oscillations in the conductance as a function of the magnetic flux, on top of the universal conductance fluctuations. At very high fluxes the interference gets suppressed and quantum Hall edge channels develop. Second, applying an electrostatic potential to one of the ring arms, nn nor npn-junctions can be realized with particle transmission due to normal tunneling or Klein tunneling. In the latter case the Aharonov-Bohm oscillations weaken for smooth barriers. Third, if potential disorder comes in to play, both Aharonov-Bohm and Klein tunneling effects rate down, up to the point where particle localization sets in.
Much of the recent enthusiasm directed towards topological insulators [1-13] as a new state of ma... more Much of the recent enthusiasm directed towards topological insulators [1-13] as a new state of matter is motivated by their hallmark feature of protected chiral edge states. In fermionic systems, Kramers degeneracy gives rise to these entities in the presence of time-reversal symmetry (TRS) [1-3, 14, 15]. In contrast, bosonic systems obeying TRS are generally assumed to be fundamentally precluded from supporting edge states [3, 16]. In this work, we dispel this perception and experimentally demonstrate counterpropagating chiral states at the edge of a time-reversal-symmetric photonic waveguide structure. The pivotal step in our approach is encoding the effective spin of the propagating states as a degree of freedom of the underlying waveguide lattice, such that our photonic topological insulator is characterised by a Z 2-type invariant. Our findings allow for fermionic properties to be harnessed in bosonic systems, thereby opening new avenues for topological physics in photonics as well as acoustics, mechanics and even matter waves.
We address the electronic properties of quantum dots in the two-dimensional α − 𝒯3 lattice when s... more We address the electronic properties of quantum dots in the two-dimensional α − 𝒯3 lattice when subjected to a perpendicular magnetic field. Implementing an infinite mass boundary condition, we first solve the eigenvalue problem for an isolated quantum dot in the low-energy, long-wavelength approximation where the system is described by an effective Dirac-like Hamiltonian that interpolates between the graphene (pseudospin 1/2) and Dice (pseudospin 1) limits. Results are compared to a full numerical (finite-mass) tight-binding lattice calculation. In a second step we analyse charge transport through a contacted α − 𝒯3 quantum dot in a magnetic field by calculating the local density of states and the conductance within the kernel polynomial and Landauer-Büttiker approaches. Thereby the influence of a disordered environment is discussed as well. Graphical abstract
Uploads
Papers by Holger Fehske