1,721,047 research outputs found
Magnetism of finite graphene samples: Mean-field theory compared with exact diagonalization and quantum Monte Carlo simulations
No full textThe magnetic properties of graphene on finite geometries are studied using a self-consistent mean-field theory of the Hubbard model. This approach is known to predict ferromagnetic edge states close to the zigzag edges in single-layer graphene quantum dots and nanoribbons. In order to assess the accuracy of this method, we perform complementary exact diagonalization and quantum Monte Carlo simulations. We observe good quantitative agreement for all quantities investigated provided that the Coulomb interaction is not too strong.ESF; Deutsche Forschungsgemeinschaft [HO 2325/4-1, WE 3649/2-1
Mott Quantum Criticality in the Anisotropic 2D Hubbard Model
No full textWe present evidence for Mott quantum criticality in an anisotropic two-dimensional system of coupled Hubbard chains at half-filling. In this scenario emerging from variational cluster approximation and cluster dynamical mean-field theory, the interchain hopping t(perpendicular to) acts as a control parameter driving the second-order critical end point T-c of the metal-insulator transition down to zero at t(perpendicular to)(c)/t similar or equal to 0.2. Below t(perpendicular to)(,)(c) the volume of the hole and electron Fermi pockets of a compensated metal vanishes continuously at the Mott transition. Above t(perpendicular to)(c), the volume reduction of the pockets is cut off by a first-order transition. We discuss the relevance of our findings to a putative quantum critical point in layered organic conductors, whose location remains elusive so far
Instanton gas approach to the Hubbard model
No full textWe consider a path integral formulation of the Hubbard model based on a Hubbard-Stratonovich transformation that couples the auxiliary field to the local electronic density. This decoupling is known to have a saddle-point structure that shows a remarkable regularity: The field configuration at each saddle point can be understood in terms of a set of elementary field configurations localized in space and imaginary time which we coin instantons. The interaction between instantons is short ranged. Here, we formulate a classical partition function for the instanton gas that has predictive power. For a given set of physical parameters, we can predict the distribution of instantons and show that the instanton number is sharply defined in the thermodynamic limit, thereby defining a unique dominant saddle point. Decoupling in the charge channel conserves SU(2) spin symmetry for each field configurations. Hence, the instanton approach provides an SU(2) spin-symmetric approximation to the Hubbard model. It fails, however, to capture the magnetic transition inherent to the Hubbard model on the honeycomb lattice despite being able to describe local moment formation. In fact, the instanton itself corresponds to local moment formation and concomitant short-ranged antiferromagnetic correlations. This aspect is also seen in the single particle spectral function that shows clear signs of the upper and lower Hubbard bands. Our instanton approach bears remarkable similarities to local dynamical approaches, such as dynamical mean-field theory, in the sense that it has the unique property of allowing for local moment formation without breaking the SU(2) spin symmetry. In contrast to local approaches, it captures short-ranged magnetic fluctuations. Furthermore, it also offers possibilities for systematic improvements by taking into account fluctuations around the dominant saddle point. Finally, we show that the saddle point structure depends upon the choice of lattice geometry. For the square lattice at half filling, the saddle-point structure reflects the itinerant to localized nature of the magnetism as a function of the coupling strength. The implications of our results for Lefschetz thimble approaches to alleviate the sign problem are also discussed.Please read the ReadMe.txt file in the provided .zip file for technical details about data processing and plotting.Funding was provided partially by Cluster of Excellence ct-qmat (Complexity and Topology in Quantum Matter
Quantum Fisher information in a strange metal
No full textProcessed data (including ones used for generating the figures) from theoretical calculations in the manuscript: "Quantum Fisher information in a strange metal" on https://arxiv.org/abs/2403.12779. Please read the 'README.md' file.We are grateful for funding support from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy through the Würzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter ct.qmat (EXC 2147, Project ID 390858490) as well as through the Collaborative Research Center SFB 1170 ToCoTronics (Project ID 258499086). We also acknowledge funding from the Deutsche Forschungsgemeinschaft via Grant No. AS120/16-1, Project No. 493886
Dynamical Signatures of Edge-State Magnetism on Graphene Nanoribbons
No full textWe investigate the edge-state magnetism of graphene nanoribbons using projective quantum Monte Carlo simulations and a self-consistent mean-field approximation of the Hubbard model. The static magnetic correlations are found to be short ranged. Nevertheless, the correlation length increases with the width of the ribbon such that already for ribbons of moderate widths we observe a strong trend towards mean-field-type ferromagnetic correlations at a zigzag edge. These correlations are accompanied by a dominant low-energy peak in the local spectral function and we propose that this can be used to detect edge-state magnetism by scanning tunneling microscopy. The dynamic spin structure factor at the edge of a ribbon exhibits an approximately linearly dispersing collective magnonlike mode at low energies that decays into Stoner modes beyond the energy scale where it merges into the particle-hole continuum
Phases and exotic phase transitions of a two-dimensional Su-Schrieffer-Heeger model
No full textData to reproduce the figures of the publication: A. Götz, M. Hohenadler, and F. F. Assaad, Phases and exotic phase transitions of a two-dimensional Su-Schrieffer-Heeger model, Phys. Rev. B 109, 195154 (2024). Please read the 'README' file.We thank the Würzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter ct.qmat (EXC 2147, Project No. 390858490) as well as the DFG under the grant AS 120/16- 1 (Project No. 493886309) that is part of the collaborative research project SFB Q-M&S funded by the Austrian Science Fund (FWF) F 86. We are grateful for funding support from the DFG funded SFB 1170 on Topological and Correlated Electronics at Surfaces and Interfaces under the Grant No. C01. The authors gratefully acknowledge the Gauss Centre for Supercomputing e.V. for funding this project by providing computing time on the GCS Supercomputer SuperMUC-NG at the Leibniz Supercomputing Centre. The authors gratefully acknowledge the scientific support and HPC resources provided by the Erlangen National High Performance Computing Center (NHR@FAU) of the Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) under NHR Project No. 80069. NHR funding is provided by federal and Bavarian state authorities. NHR@FAU hardware is partially funded by the German Research Foundation (DFG) through Grant No. 440719683
Hubbard und Kondo Gittermodelle in zwei Dimensionen : eine QMC Untersuchung
No full textThis thesis discusses mainly two Fermionic lattice systems, first a Kondo lattice with additional Hubbard interaction and second a Hubbard Hamiltonian augmented with additional spin and charge interactions.
We first introduce the Quantum Monte Carlo technique, which is then employed to study the two respective systems. We present an innovation that allows to calculate time displaced Greens functions more efficiently. Compared with previously used numerically stable algorithms the new method gains an order of magnitude in speed, but is just as precise, and very simple to implement.
In the second chapter we consider the Kondo lattice model in two dimensions at half filling. In addition to the Fermionic hopping integral t and the superexchange coupling J the role of a Coulomb repulsion U in the conduction band is investigated. We find the model to display a magnetic order-disorder transition in the U-J plane with a critical value of Jc which is decreasing as a function of U. The single-particle spectral function A(k,ω) is computed across this transition. We conclude that (i) the local screening of impurity spins determines the low-energy behavior of the spectral function and (ii) one cannot deform continuously the spectral function of the half-filled Hubbard model at J=0 to that of the Kondo insulator at J>Jc.
In the third chapter we investigate the phase diagram of a new model that exhibits a first order transition between s-wave superconducting and antiferromagnetic phases. The model, a generalized Hubbard model augmented with competing spin-spin and pair-pair interactions, was investigated using the projector quantum Monte Carlo method. Upon varying the Hubbard U from attractive to repulsive, we find a first order phase transition between superconducting and antiferromagnetic states.In dieser Arbeit werden zwei fermionische Gittermodelle diskutiert. Zum einen das Kondo-Gittermodell mit zusätzlicher Hubbard Wechselwirkung, zum anderen ein Hubbard Modell mit weiteren Spin- und Ladungswechselwirkung.
Im ersten Teil dikutieren wir die Quanten-Monte-Carlo Technik, die später zur Untersuchung der beiden Systeme verwendet wird. Eine neue Methode zur Berechnung der zeitabhängigen Greensfunktion wird vorgestellt. Verglichen mit dem zuvor benützten Algorithmus, löst die neue Technik genauso das numerische Stabilitätsproblem und ist zugleich eine Größenordnung schneller.
Im zweiten Kapitel betrachten wir das Kondo-Gittermodell in zwei Dimensionen und bei halber Füllung. Zusätzlich zur elektronischen Hüpfamplitude t und dem Superaustausch J wird die Rolle einer Coulombabstossung U im Leitungsband untersucht. Das Modell hat einen magnetischen Ordnung-Unordnungs Übergang in der U-J Ebene und der kritische Wert Jc nimmt als Funktion von U ab. Die Einteilchen-Spektralfunktion A(k,ω) wird auf beiden Seiten des Übergangs berechnet. Wir kommen zu dem Ergebnis, dass (i) das lokale Screening der f-Spins für das Niederenergieverhalten der Spektralfunktion zuständig ist und (ii) kann die Spektralfunktion des halbgefüllten Hubbard Modells bei J=0 nicht kontinuierlich zu einem Kondo Modell bei J>Jc verwendet werden.
Im dritten Kapitel untersuchen wir das Phasendiagramm eines neuen Modells, das einen Übergang erster Ordnung zwischen s-Wellen Supraleitung und Antiferromagnetismus zeigt. Bei dem Modell handelt es sich um ein Hubbard Modell, das um Spin-Spin und Ladung-Ladungs Wechselwirkungsterme erweitert wurde. Den erste Ordung Phasenübergang zwischen Supraleitung und Antiferromagnetismus findet man bei Variation des Hubbard U von attraktiv zu repulsiv
Hubbard and Heisenberg models on hyperbolic lattices - Metal-insulator transitions, global antiferromagnetism and enhanced boundary fluctuations
No full textProcessed data used for generating the figures of manuscript: "Hubbard and Heisenberg models on hyperbolic lattices - Metal-insulator transitions, global antiferromagnetism and enhanced boundary fluctuations" on arXiv: https://arxiv.org/abs/2406.03416. Please read the 'README' file.We are grateful for funding support from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy through the Würzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter ct.qmat (EXC 2147, Project ID 390858490) as well as through the Collaborative Research Center SFB 1170 ToCoTronics (Project ID 258499086)
Phase diagram of the SU(N) antiferromagnet of spin S on a square lattice
No full textData to reproduce the results of the publication: Jonas Schwab, Francesco Parisen Toldin, and Fakher F. Assaad. "Phase diagram of the SU() antiferromagnet of spin on a square lattice" Phys. Rev. B, 108:115151, Sep 2023. arXiv:2304.07329, doi:10.1103/PhysRevB.108.115151.Paper abstract: We investigate the ground state phase diagram of an SU(N)-symmetric antiferromagnetic spin model on a square lattice where each site hosts an irreducible representation of SU(N) described by a square Young tableau of rows and columns. We show that negative sign free fermion Monte Carlo simulations can be carried out for this class of quantum magnets at any and even values of . In the large- limit, the saddle point approximation favors a four-fold degenerate valence bond solid phase. In the large -limit, the semi-classical approximation points to Néel state. On a line set by in the versus phase diagram, we observe a variety of phases proximate to the Néel state. At and we observe the aforementioned four fold degenerate valence bond solid state. At a two fold degenerate spin nematic state in which the C lattice symmetry is broken down to C emerges. Finally at we observe a unique ground state that pertains to a two-dimensional version of the Affleck-Kennedy-Lieb-Tasaki state. For our specific realization, this symmetry protected topological state is characterized by an SU(18), boundary state, that has a dimerized ground state. These phases that are proximate to the Néel state are consistent with the notion of monopole condensation of the antiferromagnetic order parameter. In particular one expects spin disordered states with degeneracy set by mod(4,2S).Please read the 'README' file.This research has been funded by the Deutsche Forschungsgemeinschaft (DFG) through the Würzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter ct.qmat (EXC 2147, Project No. 390858490), the SFB1170 on Topological and Correlated Electronics at Surfaces and Interfaces (Project No. 258499086), Project No. 414456783 and Grant No. AS 120/14-1. The authors gratefully acknowledge the Gauss Centre for Supercomputing e.V. for funding this project by providing computing time on the GCS Supercomputer SuperMUC-NG at Leibniz Supercomputing Centre. The authors gratefully acknowledge the scientific support and HPC resources provided by the Erlangen National High Performance Computing Center (NHR@FAU) of the Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) under the NHR project b133ae. NHR funding is provided by federal and Bavarian state authorities. NHR@FAU hardware is partially funded by the German Research Foundation (DFG) – 440719683
Hydrodynamics of Lorentz symmetric systems: a quantum Monte Carlo study
No full textWe present a study on the hydrodynamic behavior of charge current in a Lorentz symmetric system: graphene at charge-neutrality. We compute the current profiles directly from Quantum Monte Carlo (QMC) simulations of the microscopic tight-binding model with long-range Coulomb interactions. This allows us to get results in a clean environment with all scattering channels being controlled by the parameters of the microscopic Hamiltonian and exact results delivered by QMC without further approximations. As a consequence, we can trace the emergence of continuous hy- drodynamics in the initially discrete lattice system. Special attention is paid to the emergence of macroscopic boundary conditions from microscopic details of the sample’s edges. Another important peculiarity is the decoupling of the charge current from the momentum flow in the Lorentz symmet- ric system, since the electrons and holes propagate in opposite directions with equal distribution functions. Using Boltzmann transport theory, we derive Navier-Stokes-type equations directly for the charge current, thus eliminating the need for any mechanism coupling the velocity field and charge current to explain the experimentally observed hydrodynamic flow profiles in graphene at half-filling. In this framework, the current diffusion coefficient replaces viscosity. QMC current profiles and the extracted temperature dependence for the current diffusion coefficient are in good agreement with the aforementioned theory, thus supporting our kinetic description of hydrodynamic currents in charge neutral graphene.MU (AR) thanks the DFG for financial support un- der the projects UL444/2-1, Project number 495044360 (AS120/19-1, Project number 530989922). FFA ac- knowledges financial support from the DFG through the W¨urzburg-Dresden Cluster of Excellence on Complex- ity and Topology in Quantum Matter - ct.qmat (EXC 2147, Project No. 390858490) as well as the SFB 1170 on Topological and Correlated Electronics at Surfaces and Interfaces (Project No. 258499086). KP acknowledges funding by the Deutsche Forschungsgemeinschaft (DFG) via the Emmy Noether Programme (Quantum Design grant, ME4844/1, project- id 327807255), project A04 of the Collaborative Research Center SFB 1143 (project- id 247310070), and the Cluster of Excellence on Com- plexity and Topology in Quantum Matter ct.qmat (EXC 2147, project-id 390858490). We gratefully acknowledge the Gauss Centre for Supercomputing e.V. (www.gauss- centre.eu) for funding this project by providing com- puting time for the computation of the current-current correlator on the GCS Supercomputer SUPERMUC- NG at the Leibniz Supercomputing Centre (www.lrz.de, project number pn73xu), as well as the scientific support and HPC resources provided by the Erlangen National High Performance Computing Center (NHR@FAU) of the Friedrich-Alexander-Universit¨at Erlangen-N¨urnberg (FAU) under the NHR project b133ae to carry out the SAC analysis. NHR funding is provided by federal and Bavarian state authorities. NHR@FAU hardware is par- tially funded by the German Research Foundation (DFG) – 440719683. JUWELS supercomputer was used for the calculation of E tensor. The numerical calcula- tions were carried out with the Algorithms for Lattice Fermions (ALF) library
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