Exact quantum Monte Carlo methods for correlated electron systems

Thema dieser Arbeit ist die Entwicklung und Kombination verschiedener numerischer Methoden, sowie deren Anwendung auf Probleme stark korrelierter Elektronensysteme. Solche Materialien zeigen viele interessante physikalische Eigenschaften, wie z.B. Supraleitung und magnetische Ordnung und spielen eine bedeutende Rolle in technischen Anwendungen. Es werden zwei verschiedene Modelle behandelt: das Hubbard-Modell und das Kondo-Gitter-Modell (KLM). In den letzten Jahrzehnten konnten bereits viele Erkenntnisse durch die numerische Lösung dieser Modelle gewonnen werden. Dennoch bleibt der physikalische Ursprung vieler Effekte verborgen. Grund dafür ist die Beschränkung aktueller Methoden auf bestimmte Parameterbereiche. Eine der stärksten Einschränkungen ist das Fehlen effizienter Algorithmen für tiefe Temperaturen.rnrnBasierend auf dem Blankenbecler-Scalapino-Sugar Quanten-Monte-Carlo (BSS-QMC) Algorithmus präsentieren wir eine numerisch exakte Methode, die das Hubbard-Modell und das KLM effizient bei sehr tiefen Temperaturen löst. Diese Methode wird auf den Mott-Übergang im zweidimensionalen Hubbard-Modell angewendet. Im Gegensatz zu früheren Studien können wir einen Mott-Übergang bei endlichen Temperaturen und endlichen Wechselwirkungen klar ausschließen.rnrnAuf der Basis dieses exakten BSS-QMC Algorithmus, haben wir einen Störstellenlöser für die dynamische Molekularfeld Theorie (DMFT) sowie ihre Cluster Erweiterungen (CDMFT) entwickelt. Die DMFT ist die vorherrschende Theorie stark korrelierter Systeme, bei denen übliche Bandstrukturrechnungen versagen. Eine Hauptlimitation ist dabei die Verfügbarkeit effizienter Störstellenlöser für das intrinsische Quantenproblem. Der in dieser Arbeit entwickelte Algorithmus hat das gleiche überlegene Skalierungsverhalten mit der inversen Temperatur wie BSS-QMC. Wir untersuchen den Mott-Übergang im Rahmen der DMFT und analysieren den Einfluss von systematischen Fehlern auf diesen Übergang.rnrnEin weiteres prominentes Thema ist die Vernachlässigung von nicht-lokalen Wechselwirkungen in der DMFT. Hierzu kombinieren wir direkte BSS-QMC Gitterrechnungen mit CDMFT für das halb gefüllte zweidimensionale anisotrope Hubbard Modell, das dotierte Hubbard Modell und das KLM. Die Ergebnisse für die verschiedenen Modelle unterscheiden sich stark: während nicht-lokale Korrelationen eine wichtige Rolle im zweidimensionalen (anisotropen) Modell spielen, ist in der paramagnetischen Phase die Impulsabhängigkeit der Selbstenergie für stark dotierte Systeme und für das KLM deutlich schwächer. Eine bemerkenswerte Erkenntnis ist, dass die Selbstenergie sich durch die nicht-wechselwirkende Dispersion parametrisieren lässt. Die spezielle Struktur der Selbstenergie im Impulsraum kann sehr nützlich für die Klassifizierung von elektronischen Korrelationseffekten sein und öffnet den Weg für die Entwicklung neuer Schemata über die Grenzen der DMFT hinaus.

Intermolecular and Intramolecular Charge Transfer in Functional Molecular Materials

This thesis is devoted to the investigation of inter and intramolecular charge transfer (CT) in molecular functional materials and specifically organic dyes and CT crystals. An integrated approach encompassing quantum-chemical calculations, semiempirical tools, theoretical models and spectroscopic measurements is applied to understand structure-property relationships governing the low-energy physics of these materials. Four main topics were addressed: 1) Spectral properties of organic dyes. Charge-transfer dyes are constituted by electron donor (D) and electron acceptor (A) units linked through bridge(s) to form molecules with different symmetry and dimensionality. Their low-energy physics is governed by the charge resonance between D and A groups and is effectively described by a family of parametric Hamiltonians known as essential-state models. These models account for few electronic states, corresponding to the main resonance structures of the relevant dye, leading to a simple picture that is completed introducing the coupling of the electronic system to molecular vibrations, treated in a non-adiabatic way, and an effective classical coordinate, describing polar solvation. In this work a specific essential-state model was proposed and parametrized for the dye Brilliant Green. The central issue in this work has been the definition of the diabatic states, a not trivial task for a multi-branched chromophore. In a second effort, we have used essential-state models for the description of the early-stage dynamics of excited states after ultrafast excitation. Crucial to this work is the fully non-adiabatic treatment of the coupled electronic and vibrational motion, allowing for a reliable description of the dynamics of systems showing a multistable, broken-symmetry excited state. 2) Mixed-stack CT salts. Mixed-stack (MS) CT crystals are an interesting class of multifunctional molecular materials, where D and A molecules arrange themselves to form stacks, leading to delocalized electrons in one dimension. The interplay between the intermolecular CT, electrostatic interactions, lattice phonons and molecular vibrations leads to intriguing physical properties that include (photoinduced) phase transitions, multistability, antiferromagnetism, ferroelectricity and potential multiferroicity. The standard microscopic model to describe this family of materials is the Modified Hubbard model accounting for electron-phonon coupling (Peierls coupling), electron-molecular vibrations coupling (Holstein coupling) and electrostatic interactions. We adopt and validate a method, based on DFT calculations on dimeric DA structures, to extract relevant model parameters. The approach offers a powerful tool to shed light on the complex physics of MS-CT salts. 3) Charge transfer in organic radical dipolar dyes. In collaboration with the group of Prof. Jaume Veciana (ICMAB- Barcellona), we have studied spectral properties of a special class of CT dyes with D-bridge-A structure where the acceptor group is a stable radical (of the perchlorotriphenylmethyl, PTM, family), leading to an open-shell CT dyes. These materials are of interest since they associate the electronic and optical properties of CT dyes with magnetic properties from the unpaired electron. The first effort was devoted to the parametrization of the relevant essential-state model. Two strategies were adopted, one based on the calculation of the low-energy spectral properties, the other based on the variation of ground state properties with an applied electric field. 4) The spectral properties of organic nanoparticles based on radical species are investigated in collaboration with Dr. I. Ratera (ICMAB- Barcellona). Intriguing spectroscopic behavior was observed pointing to the presence of excimer states. In an attempt to rationalize these findings, extensive calculations (TD-DFT and ZINDO) were performed. The results for the isolated dyes are validated against experimental spectra in solution. To address intermolecular interactions we studied dimeric structures in the gas phase, but the preliminary results obtained do not support excimer formation.

Prediction of hidden multiferroic order in graphene zigzag ribbons

An electronic phase with coexisting magnetic and ferroelectric order is predicted for graphene ribbons with zigzag edges. The electronic structure of the system is described with a mean-field Hubbard model that yields results very similar to those of density functional calculations. Without further approximations, the mean-field theory is recasted in terms of a BCS wave function for electron-hole pairs in the edge bands. The BCS coherence present in each spin channel is related to spin-resolved electric polarization. Although the total electric polarization vanishes, due to an internal phase locking of the BCS state, strong magnetoelectric effects are expected in this system. The formulation naturally accounts for the two gaps in the quasiparticle spectrun, Δ0 and Δ1, and relates them to the intraband and interband self-energies.

Vacancy-induced magnetism in graphene and graphene ribbons

We address the electronic structure and magnetic properties of vacancies and voids both in graphene and graphene ribbons. By using a mean-field Hubbard model, we study the appearance of magnetic textures associated with removing a single atom (vacancy) and multiple adjacent atoms (voids) as well as the magnetic interactions between them. A simple set of rules, based on the Lieb theorem, link the atomic structure and the spatial arrangement of the defects to the emerging magnetic order. The total spin S of a given defect depends on its sublattice imbalance, but some defects with S=0 can still have local magnetic moments. The sublattice imbalance also determines whether the defects interact ferromagnetically or antiferromagnetically with one another and the range of these magnetic interactions is studied in some simple cases. We find that in semiconducting armchair ribbons and two-dimensional graphene without global sublattice imbalance, there is a maximum defect density above which local magnetization disappears. Interestingly, the electronic properties of semiconducting graphene ribbons with uncoupled local moments are very similar to those of diluted magnetic semiconductors, presenting giant Zeeman splitting.

Hydrogenated graphene nanoribbons for spintronics

We show how hydrogenation of graphene nanoribbons at small concentrations can open venues toward carbon-based spintronics applications regardless of any specific edge termination or passivation of the nanoribbons. Density-functional theory calculations show that an adsorbed H atom induces a spin density on the surrounding π orbitals whose symmetry and degree of localization depends on the distance to the edges of the nanoribbon. As expected for graphene-based systems, these induced magnetic moments interact ferromagnetically or antiferromagnetically depending on the relative adsorption graphene sublattice, but the magnitude of the interactions are found to strongly vary with the position of the H atoms relative to the edges. We also calculate, with the help of the Hubbard model, the transport properties of hydrogenated armchair semiconducting graphene nanoribbons in the diluted regime and show how the exchange coupling between H atoms can be exploited in the design of novel magnetoresistive devices.

Spontaneous persistent currents in a quantum spin Hall insulator

We present a mechanism for persistent charge current. Quantum spin Hall insulators hold dissipationless spin currents in their edges so that, for a given spin orientation, a net charge current flows which is exactly compensated by the counterflow of the opposite spin. Here we show that ferromagnetic order in the edge upgrades the spin currents into persistent charge currents without applied fields. For that matter, we study the Hubbard model including Haldane-Kane-Mele spin-orbit coupling in a zigzag ribbon and consider the case of graphene. We find three electronic phases with magnetic edges that carry currents reaching 0.4 nA, comparable to persistent currents in metallic rings, for the small spin-orbit coupling in graphene. One of the phases is a valley half metal.

Interplay between sublattice and spin symmetry breaking in graphene

We study the effect of sublattice symmetry breaking on the electronic, magnetic, and transport properties of two-dimensional graphene as well as zigzag terminated one- and zero-dimensional graphene nanostructures. The systems are described with the Hubbard model within the collinear mean field approximation. We prove that for the noninteracting bipartite lattice with an unequal number of atoms in each sublattice, in-gap states still exist in the presence of a staggered on-site potential ±Δ/2. We compute the phase diagram of both 2D and 1D graphene with zigzag edges, at half filling, defined by the normalized interaction strength U/t and Δ/t, where t is the first neighbor hopping. In the case of 2D we find that the system is always insulating, and we find the Uc(Δ) curve above which the system goes antiferromagnetic. In 1D we find that the system undergoes a phase transition from nonmagnetic insulator for U

Magnetism in graphene nanoislands

We study the magnetic properties of nanometer-sized graphene structures with triangular and hexagonal shapes terminated by zigzag edges. We discuss how the shape of the island, the imbalance in the number of atoms belonging to the two graphene sublattices, the existence of zero-energy states, and the total and local magnetic moment are intimately related. We consider electronic interactions both in a mean-field approximation of the one-orbital Hubbard model and with density functional calculations. Both descriptions yield values for the ground state total spin S consistent with Lieb’s theorem for bipartite lattices. Triangles have a finite S for all sizes whereas hexagons have S=0 and develop local moments above a critical size of ≈1.5  nm.

Role of potassium orbitals in the metallic behavior of K3picene

Detailed electronic structure calculations of picene clusters doped by potassium modeling the crystalline K3picene structure show that while two electrons are completely transferred from potassium atoms to the lowest-energy unoccupied molecular orbital of pristine picene, the third one remains closely attached to both material components. Multiconfigurational analysis is necessary to show that many structures of almost degenerate total energies compete to define the cluster ground state. Our results prove that the 4s orbital of potassium should be included in any interaction model describing the material. We propose a quarter-filled two-orbital model as the most simple model capable of describing the electronic structure of K-intercalated picene. Precise solutions obtained by a development of the Lanczos method show low-energy electronic excitations involving orbitals located at different positions. Consequently, metallic transport is possible in spite of the clear dominance of interaction over hopping.

Noncollinear magnetic phases and edge states in graphene quantum Hall bars

Application of a perpendicular magnetic field to charge neutral graphene is expected to result in a variety of broken symmetry phases, including antiferromagnetic, canted, and ferromagnetic. All these phases open a gap in bulk but have very different edge states and noncollinear spin order, recently confirmed experimentally. Here we provide an integrated description of both edge and bulk for the various magnetic phases of graphene Hall bars making use of a noncollinear mean field Hubbard model. Our calculations show that, at the edges, the three types of magnetic order are either enhanced (zigzag) or suppressed (armchair). Interestingly, we find that preformed local moments in zigzag edges interact with the quantum spin Hall like edge states of the ferromagnetic phase and can induce backscattering.

The gap equations for spin singlet and triplet ferromagnetic superconductors

We derive gap equations for superconductivity in coexistence with ferromagnetism. We treat singlet and triplet states With either equal spin pairing (ESP) or opposite spin pairing (OSP) states, and study the behaviour of these states as a function of exchange splitting. For the s-wave singlet state we find that our gap equations correctly reproduce the Clogston-Chandrasekhar limiting behaviour and the phase diagram of the Baltensperger-Sarma equation (excluding the FFLO region). The singlet superconducting order parameter is shown to be independent of exchange splitting at zero temperature, as is assumed in the derivation of the Clogston-Chandrasekhar limit. P-wave triplet states of the OSP type behave similarly to the singlet state as a function of exchange splitting. On the other hand, ESP triplet states show a very different behaviour. In particular, there is no Clogston-Chandrasekhar limiting and the superconducting critical temperature, T-C, is actually increased by exchange splitting.

Gaussian quantum Monte Carlo methods for fermions and bosons

We introduce a new class of quantum Monte Carlo methods, based on a Gaussian quantum operator representation of fermionic states. The methods enable first-principles dynamical or equilibrium calculations in many-body Fermi systems, and, combined with the existing Gaussian representation for bosons, provide a unified method of simulating Bose-Fermi systems. As an application relevant to the Fermi sign problem, we calculate finite-temperature properties of the two dimensional Hubbard model and the dynamics in a simple model of coherent molecular dissociation.

Quantum phase-space simulations of fermions and bosons

We introduce a unified Gaussian quantum operator representation for fermions and bosons. The representation extends existing phase-space methods to Fermi systems as well as the important case of Fermi-Bose mixtures. It enables simulations of the dynamics and thermal equilibrium states of many-body quantum systems from first principles. As an example, we numerically calculate finite-temperature correlation functions for the Fermi Hubbard model, with no evidence of the Fermi sign problem. (c) 2005 Elsevier B.V. All rights reserved.

Gaussian phase-space representations for fermions

We introduce a positive phase-space representation for fermions, using the most general possible multimode Gaussian operator basis. The representation generalizes previous bosonic quantum phase-space methods to Fermi systems. We derive equivalences between quantum and stochastic moments, as well as operator correspondences that map quantum operator evolution onto stochastic processes in phase space. The representation thus enables first-principles quantum dynamical or equilibrium calculations in many-body Fermi systems. Potential applications are to strongly interacting and correlated Fermi gases, including coherent behavior in open systems and nanostructures described by master equations. Examples of an ideal gas and the Hubbard model are given, as well as a generic open system, in order to illustrate these ideas.

Strong electronic correlations in superconducting organic charge transfer salts

We review the role of strong electronic correlations in quasi-two-dimensional organic charge transfer salts such as (BEDT-TTF)(2)X, (BETS)(2)Y, and beta'-[Pd(dmit)(2)](2)Z. We begin by defining minimal models for these materials. It is necessary to identify two classes of material: the first class is strongly dimerized and is described by a half-filled Hubbard model; the second class is not strongly dimerized and is described by a quarter-filled extended Hubbard model. We argue that these models capture the essential physics of these materials. We explore the phase diagram of the half-filled quasi-two-dimensional organic charge transfer salts, focusing on the metallic and superconducting phases. We review work showing that the metallic phase, which has both Fermi liquid and 'bad metal' regimes, is described both quantitatively and qualitatively by dynamical mean field theory (DMFT). The phenomenology of the superconducting state is still a matter of contention. We critically review the experimental situation, focusing on the key experimental results that may distinguish between rival theories of superconductivity, particularly probes of the pairing symmetry and measurements of the superfluid stiffness. We then discuss some strongly correlated theories of superconductivity, in particular the resonating valence bond (RVB) theory of superconductivity. We conclude by discussing some of the major challenges currently facing the field. These include parameterizing minimal models, the evidence for a pseudogap from nuclear magnetic resonance (NMR) experiments, superconductors with low critical temperatures and extremely small superfluid stiffnesses, the possible spin- liquid states in kappa-(ET)(2)Cu-2(CN)(3) and beta'-[Pd(dmit)(2)](2)Z, and the need for high quality large single crystals.