Friedrich Krien

Bio: Friedrich Krien is an academic researcher from Jožef Stefan Institute. The author has contributed to research in topics: Hubbard model & Vertex (graph theory). The author has an hindex of 12, co-authored 19 publications receiving 321 citations. Previous affiliations of Friedrich Krien include Vienna University of Technology & International School for Advanced Studies.

Ries crater and suevite revisited—Observations and modeling Part II: Modeling

Abstract: We present the results of numerical modeling of the formation of the Ries crater utilizing the two hydrocodes SOVA and iSALE. These standard models allow us to reproduce crater shape, size, and morphology, and composition and extension of the continuous ejecta blanket. Some of these results cannot, however, be readily reconciled with observations: the impact plume above the crater consists mainly of molten and vaporized sedimentary rocks, containing very little material in comparison with the ejecta curtain; at the end of the modification stage, the crater floor is covered by a thick layer of impact melt with a total volume of 6–11 km3; the thickness of true fallback material from the plume inside the crater does not exceed a couple of meters; ejecta from all stratigraphic units of the target are transported ballistically; no separation of sedimentary and crystalline rocks—as observed between suevites and Bunte Breccia at Ries—is noted. We also present numerical results quantifying the existing geological hypotheses of Ries ejecta emplacement from an impact plume, by melt flow, or by a pyroclastic density current. The results show that none of these mechanisms is consistent with physical constraints and/or observations. Finally, we suggest a new hypothesis of suevite formation and emplacement by postimpact interaction of hot impact melt with water or volatile-rich sedimentary rocks.

Effective Heisenberg Model and Exchange Interaction for Strongly Correlated Systems.

Abstract: We consider the extended Hubbard model and introduce a corresponding Heisenberg-like problem written in terms of spin operators. The derived formalism is reminiscent of Anderson's idea of the effective exchange interaction and takes into account nonlocal correlation effects. The results for the exchange interaction and spin susceptibility in the magnetic phase are expressed in terms of single-particle quantities. This fact not only can be used for realistic calculations of multiband systems but also allows us to reconsider a general description of many-body effects in the most interesting physical regimes, where the physical properties of the system are dominated by collective (bosonic) fluctuations. In the strongly spin-polarized limit, when the local magnetic moment is well defined, the exchange interaction reduces to a standard expression of the density functional theory that has been successfully used in practical calculations of magnetic properties of real materials.

Single-boson exchange decomposition of the vertex function

Abstract: We present a decomposition of the two-particle vertex function of the single-band Anderson impurity model which imparts a physical interpretation of the vertex in terms of the exchange of bosons of three flavors. We evaluate the various components of the vertex for an impurity model corresponding to the half-filled Hubbard model within dynamical mean-field theory. For small values of the interaction almost the entire information encoded in the vertex function corresponds to single-boson exchange processes, which can be represented in terms of the Hedin three-leg vertex and the screened interaction. Also for larger interaction, the single-boson exchange still captures scatterings between electrons and the dominant low-energy fluctuations and provides a unified description of the vertex asymptotics. The proposed decomposition of the vertex does not require the matrix inversion of the Bethe-Salpeter equation. Therefore, it represents a computationally lighter and hence more practical alternative to the parquet decomposition.

Boson-exchange parquet solver for dual fermions

Abstract: We present and implement a parquet approximation within the dual-fermion formalism based on a partial bosonization of the dual vertex function which substantially reduces the computational cost of the calculation. The method relies on splitting the vertex exactly into single-boson exchange contributions and a residual four-fermion vertex, which physically embody, respectively, long- and short-range spatial correlations. After recasting the parquet equations in terms of the residual vertex, these are solved using the truncated-unity method of Eckhardt et al. [Phys. Rev. B 101, 155104 (2020)], which allows for a rapid convergence with the number of form factors in different regimes. While our numerical treatment of the parquet equations can be restricted to only a few Matsubara frequencies, reminiscent of Astretsov et al. [Phys. Rev. B 101, 075109 (2020)], the one- and two-particle spectral information is fully retained. In applications to the two-dimensional Hubbard model the method agrees quantitatively with a stochastic summation of diagrams over a wide range of parameters.

Conservation in two-particle self-consistent extensions of dynamical mean-field theory

Abstract: Extensions of dynamical mean-field theory (DMFT) make use of quantum impurity models as nonperturbative and exactly solvable reference systems which are essential to treat the strong electronic correlations. Through the introduction of retarded interactions on the impurity, these approximations can be made two-particle self-consistent. This is of interest for the Hubbard model because it allows to suppress the antiferromagnetic phase transition in two dimensions in accordance with the Mermin-Wagner theorem, and to include the effects of bosonic fluctuations. For a physically sound description of the latter, the approximation should be conserving. In this paper, we show that the mutual requirements of two-particle self-consistency and conservation lead to fundamental problems. For an approximation that is two-particle self-consistent in the charge and longitudinal spin channels, the double occupancy of the lattice and the impurity is no longer consistent when computed from single-particle properties. For the case of self-consistency in the charge and longitudinal as well as transversal spin channels, these requirements are even mutually exclusive so that no conserving approximation can exist. We illustrate these findings for a two-particle self-consistent and conserving DMFT approximation.

Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor

Abstract: A possible sighting of Majorana states Nearly 80 years ago, the Italian physicist Ettore Majorana proposed the existence of an unusual type of particle that is its own antiparticle, the so-called Majorana fermion. The search for a free Majorana fermion has so far been unsuccessful, but bound Majorana-like collective excitations may exist in certain exotic superconductors. Nadj-Perge et al. created such a topological superconductor by depositing iron atoms onto the surface of superconducting lead, forming atomic chains (see the Perspective by Lee). They then used a scanning tunneling microscope to observe enhanced conductance at the ends of these chains at zero energy, where theory predicts Majorana states should appear. Science, this issue p. 602; see also p. 547 Scanning tunneling microscopy is used to observe signatures of Majorana states at the ends of iron atom chains. [Also see Perspective by Lee] Majorana fermions are predicted to localize at the edge of a topological superconductor, a state of matter that can form when a ferromagnetic system is placed in proximity to a conventional superconductor with strong spin-orbit interaction. With the goal of realizing a one-dimensional topological superconductor, we have fabricated ferromagnetic iron (Fe) atomic chains on the surface of superconducting lead (Pb). Using high-resolution spectroscopic imaging techniques, we show that the onset of superconductivity, which gaps the electronic density of states in the bulk of the Fe chains, is accompanied by the appearance of zero-energy end-states. This spatially resolved signature provides strong evidence, corroborated by other observations, for the formation of a topological phase and edge-bound Majorana fermions in our atomic chains.

Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory

Abstract: Strong electronic correlations pose one of the biggest challenges to solid state theory. We review recently developed methods that address this problem by starting with the local, eminently important correlations of dynamical mean field theory (DMFT). On top of this, non-local correlations on all length scales are generated through Feynman diagrams, with a local two-particle vertex instead of the bare Coulomb interaction as a building block. With these diagrammatic extensions of DMFT long-range charge-, magnetic-, and superconducting fluctuations as well as (quantum) criticality can be addressed in strongly correlated electron systems. We provide an overview of the successes and results achieved---hitherto mainly for model Hamiltonians---and outline future prospects for realistic material calculations.

Shock metamorphism of planetary silicate rocks and sediments: Proposal for an updated classification system

Abstract: We reevaluate the systematics and geologic setting of terrestrial, lunar, Martian, and asteroidal “impactites” resulting from single or multiple impacts. For impactites derived from silicate rocks and sediments, we propose a unified and updated system of progressive shock metamorphism. “Shock-metamorphosed rocks” occur as lithic clasts or melt particles in proximal impactites at impact craters, and rarely in distal impactites. They represent a wide range of metamorphism, typically ranging from unshocked to shock melted. As the degree of shock metamorphism, at a given shock pressure, depends primarily on the mineralogical composition and the porosity of a rock or sediment sample, different shock classification systems are required for different types of planetary rocks and sediments. We define shock classification systems for eight rock and sediment classes which are assigned to three major groups of rocks and sediments (1) crystalline rocks with classes F, M, A, and U; (2) chondritic rocks (class C); and (3) sedimentary rocks and sediments with classes SR, SE, and RE. The abbreviations stand for felsic (F), mafic (M), anorthositic (A), ultramafic (U), sedimentary rocks (SR), unconsolidated sediments (SE), and regoliths (RE). In each class, the progressive stages of shock metamorphism are denominated S1 to Sx. These progressive shock stages are introduced as: S1–S7 for F, S1–S7 for M, S1–S6 for A, S1–S7 for U, S1–S7 for C, S1–S7 for SR, S1–S5 for SE, and S1–S6 for RE. S1 stands for “unshocked” and Sx (variable between S5 and S7) stands for “whole rock melting.” We propose a sequence of symbols characterizing the degree of shock metamorphism of a sample, i.e., F-S1 to F-S7 with the option to add the tabulated pressure ranges (in GPa) in parentheses.

Dual fermion approach to nonlocal correlations in the Hubbard model

Abstract: A new diagrammatic technique is developed to describe nonlocal effects (e.g., pseudogap formation) in the Hubbard-like models. In contrast to cluster approaches, this method utilizes an exact transition to the dual set of variables, and it therefore becomes possible to treat the irreducible vertices of an effective {\it single-impurity} problem as small parameters. This provides a very efficient interpolation between weak-coupling (band) and atomic limits. The antiferromagnetic pseudogap formation in the Hubbard model is correctly reproduced by just the lowest-order diagrams.