arXiv subjects

Felix Hummel

Publications and source records attributed to Felix Hummel.

At least 19 recordsLinked to original sources

arXiv2025

Exploring the accuracy of the equation-of-motion coupled-cluster band gap of solids

While the periodic equation-of-motion coupled-cluster (EOM-CC) method promises systematic improvement of electronic band gap calculations in solids, its practical application at the singles and doubles level (EOM-CCSD) is hindered by severe finite-size errors in feasible simulation cells. We present a hybrid approach combining EOM-CCSD with the computationally efficient $GW$ approximation to estimate thermodynamic limit band gaps for several insulators and semiconductors. Our method substantially reduces required cell sizes while maintaining accuracy. Comparisons with experimental gaps and self-consistent $GW$ calculations reveal that deviations in EOM-CCSD predictions correlate with reduced single excitation character of the excited many-electron states. Our work not only provides a computationally tractable approach to EOM-CC calculations in solids but also reveals fundamental insights into the role of single excitations in electronic-structure theory.

cond-mat.mtrl-sci↗

arXiv2024

Finite-size Effects in periodic EOM-CCSD for Ionization Energies and Electron Affinities: Convergence Rate and Extrapolation to the Thermodynamic Limit

We investigate the convergence of quasi-particle energies for periodic systems to the thermodynamic limit using increasingly large simulation cells corresponding to increasingly dense integration meshes in reciprocal space. The quasi-particle energies are computed at the level of equation-of-motion coupled-cluster theory for ionization (IP-EOM-CC) and electron attachment processes (EA-EOM-CC). By introducing an electronic correlation structure factor, the expected asymptotic convergence rates for systems with different dimensionality are formally derived. We rigorously test these derivations through numerical simulations for trans-Polyacetylene using IP/EA-EOM-CCSD and the G0W0@HF approximation, which confirm the predicted convergence behavior. Our findings provide a solid foundation for efficient schemes to correct finite-size errors in IP/EA-EOM-CCSD calculations.

cond-mat.mtrl-sci↗

arXiv2024

An exciting hint towards the solution of the neutron lifetime puzzle?

We revisit the neutron lifetime puzzle, a discrepancy between beam and bottle measurements of the weak neutron decay. Since both types of measurements are realized at different times after the nuclear production of free neutrons, we argue that the existence of excited states could be responsible for the different lifetimes. We elaborate on the required properties of such states and under what circumstances it is possible that they have not been experimentally identified yet.

hep-ph↗

arXiv2024

Investigating the basis set convergence of diagrammatically decomposed coupled-cluster correlation energy contributions for the uniform electron gas

We investigate the convergence of coupled-cluster correlation energies and related quantities with respect to the employed basis set size for the uniform electron gas to gain a better understanding of the basis set incompleteness error. To this end, coupled-cluster doubles (CCD) theory is applied to the three dimensional uniform electron gas for a range of densities, basis set sizes and electron numbers. We present a detailed analysis of individual, diagrammatically decomposed contributions to the amplitudes at the level of CCD theory. In particular, we show that only two terms from the amplitude equations contribute to the asymptotic large-momentum behavior of the transition structure factor, corresponding to the cusp region at short interelectronic distances. However, due to the coupling present in the amplitude equations, all decomposed correlation energy contributions show the same asymptotic convergence behavior to the complete basis set limit. These findings provide an additional rationale for the success of a recently proposed correction to the basis set incompleteness error (BSIE) of coupled-cluster theory. Lastly, we examine the BSIE in the coupled-cluster doubles plus perturbative triples [CCD(T)] method, as well as in the newly proposed coupled-cluster doubles plus complete perturbative triples [CCD(cT)] method.

cond-mat.mtrl-sci↗

arXiv2023

Estimating melting curves for Cu and Al from simulations at a single state point

Determining the melting curves of materials up to high pressures has long been a challenge experimentally and theoretically. A large class of materials, including most metals, has been shown to exhibit hidden scale invariance, an approximate scale invariance of the potential-energy landscape that is not obvious from the Hamiltonian. For these materials the isomorph theory allows the identification of curves in the phase diagram along which structural and dynamical properties are invariant to a good approximation when expressed in appropriately scaled form. These curves, the isomorphs, can also be used as the basis for constructing accurate melting curves from simulations at a single state point [U. R. Pedersen et al., Nat. Comm. 7, 12386 (2016)]. In this work we apply this method to the metals Cu simulated using the effective medium theory and Al simulated using density functional theory (DFT). For Cu the method works very well and is validated using two-phase melting point simulations. For Al there are likewise good isomorphs, and the method generates the melting curve accurately as compared to previous experimental and DFT results. In support of a recent suggestion of Hong and van de Walle [Phys. Rev. B 100, 140102 (2019)], we finally suggest that the tendency for the density-scaling exponent $\gamma$ to decrease with increasing density in metals implies that metals in general will undergo re-entrant melting, i.e., have a maximum of melting temperature as a function of pressure.

cond-mat.mtrl-sci↗

arXiv2022

On the chemical potential of many-body perturbation theory in extended systems

Many methods for computing electronic correlation effects at finite temperature are related to many-body perturbation theory in the grand-canonical ensemble. In most applications, however, the average number of electrons is known rather than the chemical potential, requiring that expensive correlation calculations must be repeated iteratively in search for the chemical potential that yields the desired average number of electrons. In extended systems with mobile charges, however, the long-ranged electrostatic interaction should guarantee that the average ratio of negative and positive charges is one for any finite chemical potential. All properties per electron are virtually independent of the chemical potential, as for instance in an electric wire at different voltage potentials. This work shows that the infinite-size limit of the exchange-correlation free energy agrees with the infinite-size limit of the exchange-correlation grand potential at a non-interacting chemical potential. The latter requires only one expensive correlation calculation for each system size. Analogous to classical simulations of long-range-interacting particles, this work uses a regularization of the Coulomb interaction such that each electron on average interacts only with as many electrons as there are electrons in the simulation, avoiding interactions with periodic images. Numerical calculations of the warm uniform electron gas have been conducted with the Spencer--Alavi regularization employing the finite-temperature Hartree approximation for the self-consistent field and linearized finite-temperature direct-ring coupled cluster doubles for treating correlation.

cond-mat.mtrl-sci↗

arXiv2022

Reduction Methods in Climate Dynamics -- A Brief Review

We review a range of reduction methods that have been, or may be useful for connecting models of the Earth's climate system of differing complexity. We particularly focus on methods where rigorous reduction is possible. We aim to highlight the main mathematical ideas of each reduction method and also provide several benchmark examples from climate modelling.

math.DS↗

arXiv2022

Geometric blow-up of a dynamic Turing instability in the Swift-Hohenberg equation

We present a rigorous analysis of the slow passage through a Turing bifurcation in the Swift-Hohenberg equation using a novel approach based on geometric blow-up. We show that the formally derived multiple scales ansatz which is known from classical modulation theory can be adapted for use in the fast-slow setting, by reformulating it as a blow-up transformation. This leads to dynamically simpler modulation equations posed in the blown-up space, via a formal procedure which directly extends the established approach to the time-dependent setting. The modulation equations take the form of non-autonomous Ginzburg-Landau equations, which can be analysed within the blow-up. The asymptotics of solutions in weighted Sobelev spaces are given in two different cases: (i) A symmetric case featuring a delayed loss of stability, and (ii) A second case in which the symmetry is broken by a source term. In order to characterise the dynamics of the Swift-Hohenberg equation itself we derive rigorous estimates on the error of the dynamic modulation approximation. These estimates are obtained by bounding weak solutions to an evolution equation for the error which is also posed in the blown-up space. Using the error estimates obtained, we are able to infer the asymptotics of a large class of solutions to the dynamic Swift-Hohenberg equation. We provide rigorous asymptotics for solutions in both cases (i) and (ii). We also prove the existence of the delayed loss of stability in the symmetric case (i), and provide a lower bound for the delay time.

math.DS↗

arXiv2022

Geometric analysis of fast-slow PDEs with fold singularities via Galerkin discretisation

We study a singularly perturbed fast-slow system of two partial differential equations (PDEs) of reaction-diffusion type on a bounded domain via Galerkin discretisation. We assume that the reaction kinetics in the fast variable realise a generic fold singularity, whereas the slow variable takes the role of a dynamic bifurcation parameter, thus extending the classical analysis of the singularly perturbed fold. Our approach combines a spectral Galerkin discretisation with techniques from geometric singular perturbation theory which are applied to the resulting high-dimensional systems of ordinary differential equations. In particular, we show the existence of invariant slow manifolds in the phase space of the original system of PDEs away from the fold singularity, while the passage past the singularity of the Galerkin manifolds obtained after discretisation is described by geometric desingularisation, or blow-up. Finally, we discuss the relation between these Galerkin manifolds and the underlying slow manifolds.

math.AP↗

arXiv2022

Interface to high-performance periodic coupled-cluster theory calculations with atom-centered, localized basis functions

Coupled cluster (CC) theory is often considered the gold standard of quantum-chemistry. For solids, however, the available software is scarce. We present CC-aims, which can interface ab initio codes with localized atomic orbitals and the CC for solids (CC4S) code by the group of A. Grüneis. CC4S features a continuously growing selection of wave function-based methods including perturbation and CC theory. The CC-aims interface was developed for the FHI-aims code (https://fhi-aims.org) but is implemented such that other codes may use it as a starting point for corresponding interfaces. As CC4S offers treatment of both molecular and periodic systems, the CC-aims interface is a valuable tool, where DFT is either too inaccurate or too unreliable, in theoretical chemistry and materials science alike.

cond-mat.mtrl-sci↗

arXiv2021

Surface science using coupled cluster theory via local Wannier functions and in-RPA-embedding: the case of water on graphitic carbon nitride

A first-principles study of the adsorption of a single water molecule on a layer of graphitic carbon nitride employing an embedding approach is presented. The embedding approach involves an algorithm to obtain localized Wannier orbitals of various types expanded in a plane-wave basis and intrinsic atomic orbital projectors. The localized occupied orbitals are employed in combination with unoccupied natural orbitals to perform many-electron perturbation theory calculations of local fragments. The fragments are comprised of a set of localized orbitals close to the adsorbed water molecule. Although the surface model contains more than 100 atoms in the simulation cell, the employed fragments are small enough to allow for calculations using high-level theories up to the coupled cluster ansatz with single, double and perturbative triple particle-hole excitation operators (CCSD(T)). To correct for the missing long-range correlation energy contributions to the adsorption energy, we embed CCSD(T) theory into the direct random phase approximation, yielding rapidly convergent adsorption energies with respect to the fragment size. Convergence of computed binding energies with respect to the virtual orbital basis set is achieved employing a number of recently developed techniques. Moreover, we discuss fragment size convergence for a range of approximate many-electron perturbation theories. The obtained benchmark results are compared to a number of density functional calculations.

physics.chem-ph↗

arXiv2021

Elliptic and Parabolic Boundary Value Problems in Weighted Function Spaces

In this paper we study elliptic and parabolic boundary value problems with inhomogeneous boundary conditions in weighted function spaces of Sobolev, Bessel potential, Besov and Triebel-Lizorkin type. As one of the main results, we solve the problem of weighted $L_{q}$-maximal regularity in weighted Besov and Triebel-Lizorkin spaces for the parabolic case, where the spatial weight is a power weight in the Muckenhoupt $A_{\infty}$-class. In Besov space case we have the restriction that the microscopic parameter equals to $q$. Going beyond the $A_{p}$-range, where $p$ is the integrability parameter of the Besov or Triebel-Lizorkin space under consideration, yields extra flexibility in the sharp regularity of the boundary inhomogeneities. This extra flexibility allows us to treat rougher boundary data and provides a quantitative smoothing effect on the interior of the domain. The main ingredient is an analysis of anisotropic Poisson operators.

math.AP↗

arXiv2021

Connecting a direct and a Galerkin approach to slow manifolds in infinite dimensions

In this paper, we study slow manifolds for infinite-dimensional evolution equations. We compare two approaches: an abstract evolution equation framework and a finite-dimensional spectral Galerkin approximation. We prove that the slow manifolds constructed within each approach are asymptotically close under suitable conditions. The proof is based upon Lyapunov-Perron methods and a comparison of the local graphs for the slow manifolds in scales of Banach spaces. In summary, our main result allows us to change between different characterizations of slow invariant manifolds, depending upon the technical challenges posed by particular fast-slow systems.

math.DS↗

arXiv2020

Boundary Value Problems of Elliptic and Parabolic Type with Boundary Data of Negative Regularity

We study elliptic and parabolic boundary value problems in spaces of mixed scales with mixed smoothness on the half space. The aim is to solve boundary value problems with boundary data of negative regularity and to describe the singularities of solutions at the boundary. To this end, we derive mapping properties of Poisson operators in mixed scales with mixed smoothness. We also derive $\mathcal{R}$-sectoriality results for homogeneous boundary data in the case that the smoothness in normal direction is not too large.

math.AP↗

arXiv2020

A periodic equation-of-motion coupled-cluster implementation applied to $F$-centers in alkaline earth oxides

We present an implementation of equation of motion coupled-cluster singles and doubles (EOM-CCSD) theory using periodic boundary conditions and a plane wave basis set. Our implementation of EOM-CCSD theory is applied to study $F$-centers in alkaline earth oxides employing a periodic supercell approach. The convergence of calculated electronic excitation energies for neutral color centers in MgO, CaO and SrO crystals with respect to orbital basis set and system size is explored. We discuss extrapolation techniques that approximate excitation energies in the complete basis set limit and reduce finite size errors. Our findings demonstrate that EOM-CCSD theory can predict optical absorption energies of $F$-centers in good agreement with experiment. Furthermore, we discuss calculated emission energies corresponding to the decay from triplet to singlet states, responsible for the photoluminescence properties. Our findings are compared to experimental and theoretical results available in literature.

cond-mat.mtrl-sci↗

arXiv2020

Slow Manifolds for Infinite-Dimensional Evolution Equations

We extend classical finite-dimensional Fenichel theory in two directions to infinite dimensions. Under comparably weak assumptions we show that the solution of an infinite-dimensional fast-slow system is approximated well by the corresponding slow flow. After that we construct a two-parameter family of slow manifolds $S_{ε,ζ}$ under more restrictive assumptions on the linear part of the slow equation. The second parameter $ζ$ does not appear in the finite-dimensional setting and describes a certain splitting of the slow variable space in a fast decaying part and its complement. The finite-dimensional setting is contained as a special case in which $S_{ε,ζ}$ does not depend on $ζ$. Finally, we apply our new techniques to three examples of fast-slow systems of partial differential equations.

math.DS↗

arXiv2020

Sample Paths of White Noise in Spaces with Dominating Mixed Smoothness

The sample paths of white noise are proved to be elements of certain Besov spaces with dominating mixed smoothness. Unlike in isotropic spaces, here the regularity does not get worse with increasing space dimension. Consequently, white noise is actually much smoother than the known sharp regularity results in isotropic spaces suggest. An application of our techniques yields new results for the regularity of solutions of Poisson and heat equation on the half space with boundary noise. The main novelty is the flexible treatment of the interplay between the singularity at the boundary and the smoothness in tangential, normal and time direction.

math.PR↗

arXiv2020

Applying the Coupled-Cluster Ansatz to Solids and Surfaces in the Thermodynamic Limit

Modern electronic structure theories can predict and simulate a wealth of phenomena in surface science and solid-state physics. In order to allow for a direct comparison with experiment, such ab initio predictions have to be made in the thermodynamic limit, substantially increasing the computational cost of many-electron wave-function theories. Here, we present a method that achieves thermodynamic limit results for solids and surfaces using the "gold standard" coupled cluster ansatz of quantum chemistry with unprecedented efficiency. We study the energy difference between carbon diamond and graphite crystals, adsorption energies of water on h-BN, as well as the cohesive energy of the Ne solid, demonstrating the increased efficiency and accuracy of coupled cluster theory for solids and surfaces.

cond-mat.mtrl-sci↗