Spontaneous particle-hole symmetry breaking of correlated fermions on the Lieb lattice

We study spinless fermions with nearest-neighbor repulsive interactions ($t$-$V$ model) on the two-dimensional three-band Lieb lattice. At half-filling, the free electronic band structure consists of a flat band at zero energy and a single cone with linear dispersion. The flat band is expected to be unstable upon inclusion of electronic correlations, and a natural channel is charge order. However, due to the three-orbital unit cell, commensurate charge order implies an imbalance of electron and hole densities and therefore doping away from half-filling. Our numerical results show that below a finite-temperature Ising transition a charge density wave with one electron and two holes per unit cell and its partner under particle-hole transformation are spontaneously generated. Our calculations are based on recent advances in auxiliary-field and continuous-time quantum Monte Carlo simulations that allow sign-free simulations of spinless fermions at half-filling. It is argued that particle-hole symmetry breaking provides a route to access levels of finite doping, without introducing a sign problem.Comment: 9 pages, 6 figures, added data for strong Coulomb repulsion and classical Ising-limi

How to verify the precision of density-functional-theory implementations via reproducible and universal workflows

In the past decades many density-functional theory methods and codes adopting periodic boundary conditions have been developed and are now extensively used in condensed matter physics and materials science research. Only in 2016, however, their precision (i.e., to which extent properties computed with different codes agree among each other) was systematically assessed on elemental crystals: a first crucial step to evaluate the reliability of such computations. We discuss here general recommendations for verification studies aiming at further testing precision and transferability of density-functional-theory computational approaches and codes. We illustrate such recommendations using a greatly expanded protocol covering the whole periodic table from Z=1 to 96 and characterizing 10 prototypical cubic compounds for each element: 4 unaries and 6 oxides, spanning a wide range of coordination numbers and oxidation states. The primary outcome is a reference dataset of 960 equations of state cross-checked between two all-electron codes, then used to verify and improve nine pseudopotential-based approaches. Such effort is facilitated by deploying AiiDA common workflows that perform automatic input parameter selection, provide identical input/output interfaces across codes, and ensure full reproducibility. Finally, we discuss the extent to which the current results for total energies can be reused for different goals (e.g., obtaining formation energies).Comment: Main text: 23 pages, 4 figures. Supplementary: 68 page

Common workflows for computing material properties using different quantum engines

The prediction of material properties based on density-functional theory has become routinely common, thanks, in part, to the steady increase in the number and robustness of available simulation packages. This plurality of codes and methods is both a boon and a burden. While providing great opportunities for cross-verification, these packages adopt different methods, algorithms, and paradigms, making it challenging to choose, master, and efficiently use them. We demonstrate how developing common interfaces for workflows that automatically compute material properties greatly simplifies interoperability and cross-verification. We introduce design rules for reusable, code-agnostic, workflow interfaces to compute well-defined material properties, which we implement for eleven quantum engines and use to compute various material properties. Each implementation encodes carefully selected simulation parameters and workflow logic, making the implementer’s expertise of the quantum engine directly available to non-experts. All workflows are made available as open-source and full reproducibility of the workflows is guaranteed through the use of the AiiDA infrastructure.This work is supported by the MARVEL National Centre of Competence in Research (NCCR) funded by the Swiss National Science Foundation (grant agreement ID 51NF40-182892) and by the European Union’s Horizon 2020 research and innovation program under Grant Agreement No. 824143 (European MaX Centre of Excellence “Materials design at the Exascale”) and Grant Agreement No. 814487 (INTERSECT project). We thank M. Giantomassi and J.-M. Beuken for their contributions in adding support for PseudoDojo tables to the aiida-pseudo (https://github.com/aiidateam/aiida-pseudo) plugin. We also thank X. Gonze, M. Giantomassi, M. Probert, C. Pickard, P. Hasnip, J. Hutter, M. Iannuzzi, D. Wortmann, S. Blügel, J. Hess, F. Neese, and P. Delugas for providing useful feedback on the various quantum engine implementations. S.P. acknowledges support from the European Unions Horizon 2020 Research and Innovation Programme, under the Marie Skłodowska-Curie Grant Agreement SELPH2D No. 839217 and computer time provided by the PRACE-21 resources MareNostrum at BSC-CNS. E.F.-L. acknowledges the support of the Norwegian Research Council (project number 262339) and computational resources provided by Sigma2. P.Z.-P. thanks to the Faraday Institution CATMAT project (EP/S003053/1, FIRG016) for financial support. KE acknowledges the Swiss National Science Foundation (grant number 200020-182015). G.Pi. and K.E. acknowledge the swissuniversities “Materials Cloud” (project number 201-003). Work at ICMAB is supported by the Severo Ochoa Centers of Excellence Program (MICINN CEX2019-000917-S), by PGC2018-096955-B-C44 (MCIU/AEI/FEDER, UE), and by GenCat 2017SGR1506. B.Z. thanks to the Faraday Institution FutureCat project (EP/S003053/1, FIRG017) for financial support. J.B. and V.T. acknowledge support by the Joint Lab Virtual Materials Design (JLVMD) of the Forschungszentrum Jülich.Peer reviewe

Numerische Untersuchung von Schwere-Fermionen-Systemen und korrelierten topologischen Isolatoren

In this thesis, we investigate aspects of the physics of heavy-fermion systems and correlated topological insulators. We numerically solve the interacting Hamiltonians that model the physical systems using quantum Monte Carlo algorithms to access both ground-state and finite-temperature observables. Initially, we focus on the metamagnetic transition in the Kondo lattice model for heavy fermions. On the basis of the dynamical mean-field theory and the dynamical cluster approximation, our calculations point towards a continuous transition, where the signatures of metamagnetism are linked to a Lifshitz transition of heavy-fermion bands. In the second part of the thesis, we study various aspects of magnetic pi fluxes in the Kane-Mele-Hubbard model of a correlated topological insulator. We describe a numerical measurement of the topological index, based on the localized mid-gap states that are provided by pi flux insertions. Furthermore, we take advantage of the intrinsic spin degree of freedom of a pi flux to devise instances of interacting quantum spin systems. In the third part of the thesis, we introduce and characterize the Kane-Mele-Hubbard model on the pi flux honeycomb lattice. We place particular emphasis on the correlations effects along the one-dimensional boundary of the lattice and compare results from a bosonization study with finite-size quantum Monte Carlo simulations.Gegenstand der vorliegenden Arbeit ist die Untersuchung von Aspekten der Physik schwerer Fermionen und korrelierter topologischer Isolatoren. Wir lösen den wechselwirkenden Hamiltonoperator, der das jeweilige System modelliert, mithilfe von Quanten-Monte-Carlo-Algorithmen, um Erwartungswerte sowohl im Grundzustand als auch im thermisch angeregten Zustand zu erhalten. Zunächst richten wir das Augenmerk auf den metamagnetischen Übergang im Kondo-Gitter-Model für schwere Fermionen. Unsere Rechnungen basieren auf der dynamischen Mean-Field-Theorie und der dynamischen Cluster-Näherung. Sie weisen auf einen kontinuierlichen Übergang hin, der die metamagnetischen Merkmale mit einem Lifshitz-Übergang in der Bandstruktur der schweren Fermionen verbindet. Im zweiten Teil der Arbeit untersuchen wir verschiedene Facetten von magnetischen pi-Flüssen im Kane-Mele-Hubbard-Modell des korrelierten topologischen Isolators. Wir beschreiben eine numerische Messung der topologischen Invariante. Diese Messung beruht auf der Tatsache, dass das Einfügen von pi-Flüssen lokalisierte Zustände in der Mitte der Bandlücke des Isolators erzeugt. Darüberhinaus verwenden wir den intrinsischen Spinfreiheitsgrad eines pi-Flusses, um wechselwirkende Spinmodelle zu realisieren. Im dritten Teil der Arbeit stellen wir das Kane-Mele-Modell auf dem hexagonalen pi-Fluss-Gitter vor und charakterisieren es. Wir legen besonderen Schwerpunkt auf Wechselwirkungseffekte entlang des eindimensionalen Randes des Gitters und vergleichen die Ergebnisse einer Bosonisierungsstudie mit Quanten-Monte-Carlo-Simulationen auf endlichen Gittern

The ALF (Algorithms for Lattice Fermions) project release 1.0. Documentation for the auxiliary field quantum Monte Carlo code

The Algorithms for Lattice Fermions package provides a general code for the finite temperature auxiliary field quantum Monte Carlo algorithm. The code is engineered to be able to simulate any model that can be written in terms of sums of single-body operators, of squares of single-body operators and single-body operators coupled to an Ising field with given dynamics. We provide predefined types that allow the user to specify the model, the Bravais lattice as well as equal time and time displaced observables. The code supports an MPI implementation. Examples such as the Hubbard model on the honeycomb lattice and the Hubbard model on the square lattice coupled to a transverse Ising field are provided and discussed in the documentation. We furthermore discuss how to use the package to implement the Kondo lattice model and the $SU(N)$-Hubbard-Heisenberg model. One can download the code from our Git instance at https://alf.physik.uni-wuerzburg.de and sign in to file issues