Das Verstaendnis dafuer, welche Freiheitsgrade fuer das Eingeschlossensein der Quarks von Bedeutung sind, ist ein altbekanntes Problem. Da weithin angenommen wird, dass das Zentrum der Eichgruppe eine bedeutende Rolle spielt, ist es interessant, eine Theorie mit einem trivialen Zentrum zu untersuchen. Das einfachste Modell, um dieses Problem zu untersuchen, ist eine Theorie mit ungeradzahliger Dimension der Darstellung der Eichgruppe SU(2). Theorien mit einem trivialen Zentrum werden schon seit langer Zeit in zwei verschiedenen Diskretisierungen untersucht: die adjungierte Wilson-Wirkung und die Villain-Wirkung. Es stellte sich heraus, dass sie aus zweierlei Gruenden problematisch sind. Zunaechst zeigte sich, dass in beiden Fällen ein bulk-Phasenuebergang den physikalischen Phasenuebergang bei endlicher Temperatur ueberschattet. Darueberhinaus erwies es sich im Falle der Villain-Theorie, dass die Anwesenheit von Twist-Sektoren fuer die Konstruktion eines ergodischen Algorithmus problematisch sein kann. Die Gitter-Artefakte, die den bulk-Phasenuebergang verursachen, wurden mit Z(2) Monopolen identifiziert. Diese Monopole koennen mit Hilfe eines entsprechenden chemischen Potentials unterdrueckt werden. Eine erste Untersuchung des Phasenuebergangs bei endlicher Temperatur durch andere Autoren wurde nur im Falle der Villain-Wirkung durchgefuehrt, wobei in dieser Untersuchung die Twist-Sektoren ohne Beruecksichtigung blieben. In der vorliegenden Arbeit untersuchen wir nichtstoerungstheoretisch die Wilson-Wirkung in der adjungierten Darstellung der Eichgruppe SU(2) mit einem chemischen Potential, welches die Z(2)-Monopole bei nicht verschwindender Temperatur und bei Temperatur Null unterdrueckt. Wir untersuchen hierbei die Auswirkungen des chemischen Potentials lambda auf einige Observable. Fuer hinreichend grosse lambda zeigen die Observablen keine Diskontinuitaet in der adjungierten Kopplung. In diesem Gebiet des Phasendiagramms untersuchen wir, meist eingeschraenkt auf den trivialen Twist-Sektor, die Existenz eines Phasenuebergangs bei endlicher Temperatur. Um diesen Phasenuebergang zu identifizieren, gelingt es uns, einen neuen Ordungsparameter zu definieren, den wir erfolgreich auch in der fundamentalen Darstellung der SU(2) testen. Ferner analysieren wir die raeumliche Verteilung der fundamentalen Polyakov-loop-Variable und des Pisaer Unordnungs-Operators, welcher die Kondensation magnetischer Ladungen beschreibt. Die Ergebnisse, die wir mit diesen Untersuchungsmethoden erhielten, lassen auf einen vom bulk-Phasenuebergang entkoppelten Phasenuebergang bei endlicher Temperatur oder einen cross-over schliessen. / The understanding of which degrees of freedom are relevant for the confinement of quarks is a long standing problem. Since it is widely believed that the center of the gauge group plays an important role, it is interesting to study a theory with a trivial center. The simplest model to investigate this problem is provided by a theory in an odd-dimensional representation of the gauge group SU(2). Center-blind theories were studied long time ago in two different discretizations, the adjoint Wilson and the Villain action, and they turned out to be problematic for two reasons. In both cases a bulk phase transition was shown to overshadow the physical finite temperature one. Another feature, pointed out in the Villain case, was the presence of twist sectors, which could cause difficulties in the construction of an ergodic algorithm. The lattice artifacts responsible for the bulk phase transition were identified with Z(2) monopoles and they could be suppressed by the use of an appropriate chemical potential. A preliminary investigation of the finite temperature phase transition by other authors was done only in the Villain case and without taking care of the twist sectors. In this thesis we perform a lattice study of the Wilson action in the adjoint representation of the gauge group SU(2) with a chemical potential, which suppresses the Z(2) monopoles at zero and non-zero temperature. We investigate the effects of the chemical potential lambda on some observables. For large enough lambda at vanishing temperature the observables do not show any discontinuity in the adjoint coupling. In this region we study the existence of a finite temperature phase transition restricting ourselves mainly to the trivial twist sector. In order to detect this phase transition we are able to define a new order parameter, which we successfully test also for the case of the fundamental representation of SU(2). Furthermore we analyze the spatial distribution of the fundamental Polyakov loop and the Pisa disorder operator which detects the condensation of magnetic charges. These different tools provide an indication for a finite temperature phase transition or crossover decoupled from the bulk phase transition.

Solid state physics comprises many interesting physical phenomena driven by the complex interplay of the crystal structure, magnetic and orbital degrees of freedom, quantum fluctuations and correlation. The discovery of materials which exhibit exotic phenomena like low dimensional magnetism, superconductivity, thermoelectricity or multiferroic behavior leads to various applications which even directly influence our daily live. For such technical applications and the purposive modification of materials, the understanding of the underlying mechanisms in solids is a precondition. Nowadays DFT based band structure programs become broadly available with the possibility to calculate systems with several hundreds of atoms in reasonable time scales and high accuracy using standard computers due to the rapid technical and conceptional development in the last decades. These improvements allow to study physical properties of solids from their crystal structure and support the search for underlying mechanisms of different phenomena from microscopic grounds. This thesis focuses on the theoretical description of low dimensional magnets and intermetallic compounds. We combine DFT based electronic structure and model calculations to develop the magnetic properties of the compounds from microscopic grounds. The developed, intuitive pictures were challenged by model simulations with various experiments, probing microscopic and macroscopic properties, such as thermodynamic measurements, high field magnetization, nuclear magnetic resonance or electron spin resonance experiments. This combined approach allows to investigate the close interplay of the crystal structure and the magnetic properties of complex materials in close collaboration with experimentalists. In turn, the systematic variation of intrinsic parameters by substitution or of extrinsic factors, like magnetic field, temperature or pressure is an efficient way to probe the derived models. Especially pressure allows a continuous change of the crystal structure on a rather large energy scale without the chemical complexity of substitution, thus being an ideal tool to consistently alter the electronic structure in a controlled way. Our theoretical results not only provide reliable descriptions of real materials, exhibiting disorder, partial site occupation and/or strong correlations, but also predict fascinating phenomena upon extreme conditions. In parts this theoretical predictions were already confirmed by own experiments on large scale facilities. Whereas in the first part of this work the main purpose was to develop reliable magnetic models of low dimensional magnets, in the second part we unraveled the underlying mechanism for different phase transitions upon pressure. In more detail, the first part of this thesis is focused on the magnetic ground states of spin 1/2 transition metal compounds which show fascinating phase diagrams with many unusual ground states, including various types of magnetic order, like helical states exhibiting different pitch angles, driven by the intimate interplay of structural details and quantum fluctuations. The exact arrangement and the connection of the magnetically active building blocks within these materials determine the hybridization, orbital occupation, and orbital orientation, this way altering the exchange paths and strengths of magnetic interaction within the system and consequently being crucial for the formation of the respective ground states. The spin 1/2 transition metal compounds, which have been investigated in this work, illustrate the great variety of exciting phenomena fueling the huge interest in this class of materials. We focused on cuprates with magnetically active CuO4 plaquettes, mainly arranged into edge sharing geometries. The influence of structural peculiarities, as distortion, folding, changed bonding angles, substitution or exchanged ligands has been studied with respect to their relevance for the magnetic ground state. Besides the detailed description of the magnetic ground states of selected compounds, we attempted to unravel the origin for the formation of a particular magnetic ground state by deriving general trends and relations for this class of compounds. The details of the treatment of the correlation and influence of structural peculiarities like distortion or the bond angles are evaluated carefully. In the second part of this work we presented the results of joint theoretical and experimental studies for intermetallic compounds, all exhibiting an isostructural phase transition upon pressure. Many different driving forces for such phase transitions are known like quantum fluctuations, valence instabilities or magnetic ordering. The combination of extensive computational studies and high pressure XRD, XAS and XMCD experiments using synchrotron radiation reveals completely different underlying mechanism for the onset of the phase transitions in YCo5, SrFe2As2 and EuPd3Bx. This thesis demonstrates on a series of complex compounds that the combination of ab-initio electronic structure calculations with numerical simulations and with various experimental techniques is an extremely powerful tool for a successful description of the intriguing quantum phenomena in solids. This approach is able to reduce the complex behavior of real materials to simple but appropriate models, this way providing a deep understanding for the underlying mechanisms and an intuitive picture for many phenomena. In addition, the close interaction of theory and experiment stimulates the improvement and refinement of the methods in both areas, pioneering the grounds for more and more precise descriptions. Further pushing the limits of these mighty techniques will not only be a precondition for the success of fundamental research at the frontier between physics and chemistry, but also enables an advanced material design on computational grounds.

Solid state physics comprises many interesting physical phenomena driven by the complex interplay of the crystal structure, magnetic and orbital degrees of freedom, quantum fluctuations and correlation. The discovery of materials which exhibit exotic phenomena like low dimensional magnetism, superconductivity, thermoelectricity or multiferroic behavior leads to various applications which even directly influence our daily live. For such technical applications and the purposive modification of materials, the understanding of the underlying mechanisms in solids is a precondition. Nowadays DFT based band structure programs become broadly available with the possibility to calculate systems with several hundreds of atoms in reasonable time scales and high accuracy using standard computers due to the rapid technical and conceptional development in the last decades. These improvements allow to study physical properties of solids from their crystal structure and support the search for underlying mechanisms of different phenomena from microscopic grounds. This thesis focuses on the theoretical description of low dimensional magnets and intermetallic compounds. We combine DFT based electronic structure and model calculations to develop the magnetic properties of the compounds from microscopic grounds. The developed, intuitive pictures were challenged by model simulations with various experiments, probing microscopic and macroscopic properties, such as thermodynamic measurements, high field magnetization, nuclear magnetic resonance or electron spin resonance experiments. This combined approach allows to investigate the close interplay of the crystal structure and the magnetic properties of complex materials in close collaboration with experimentalists. In turn, the systematic variation of intrinsic parameters by substitution or of extrinsic factors, like magnetic field, temperature or pressure is an efficient way to probe the derived models. Especially pressure allows a continuous change of the crystal structure on a rather large energy scale without the chemical complexity of substitution, thus being an ideal tool to consistently alter the electronic structure in a controlled way. Our theoretical results not only provide reliable descriptions of real materials, exhibiting disorder, partial site occupation and/or strong correlations, but also predict fascinating phenomena upon extreme conditions. In parts this theoretical predictions were already confirmed by own experiments on large scale facilities. Whereas in the first part of this work the main purpose was to develop reliable magnetic models of low dimensional magnets, in the second part we unraveled the underlying mechanism for different phase transitions upon pressure. In more detail, the first part of this thesis is focused on the magnetic ground states of spin 1/2 transition metal compounds which show fascinating phase diagrams with many unusual ground states, including various types of magnetic order, like helical states exhibiting different pitch angles, driven by the intimate interplay of structural details and quantum fluctuations. The exact arrangement and the connection of the magnetically active building blocks within these materials determine the hybridization, orbital occupation, and orbital orientation, this way altering the exchange paths and strengths of magnetic interaction within the system and consequently being crucial for the formation of the respective ground states. The spin 1/2 transition metal compounds, which have been investigated in this work, illustrate the great variety of exciting phenomena fueling the huge interest in this class of materials. We focused on cuprates with magnetically active CuO4 plaquettes, mainly arranged into edge sharing geometries. The influence of structural peculiarities, as distortion, folding, changed bonding angles, substitution or exchanged ligands has been studied with respect to their relevance for the magnetic ground state. Besides the detailed description of the magnetic ground states of selected compounds, we attempted to unravel the origin for the formation of a particular magnetic ground state by deriving general trends and relations for this class of compounds. The details of the treatment of the correlation and influence of structural peculiarities like distortion or the bond angles are evaluated carefully. In the second part of this work we presented the results of joint theoretical and experimental studies for intermetallic compounds, all exhibiting an isostructural phase transition upon pressure. Many different driving forces for such phase transitions are known like quantum fluctuations, valence instabilities or magnetic ordering. The combination of extensive computational studies and high pressure XRD, XAS and XMCD experiments using synchrotron radiation reveals completely different underlying mechanism for the onset of the phase transitions in YCo5, SrFe2As2 and EuPd3Bx. This thesis demonstrates on a series of complex compounds that the combination of ab-initio electronic structure calculations with numerical simulations and with various experimental techniques is an extremely powerful tool for a successful description of the intriguing quantum phenomena in solids. This approach is able to reduce the complex behavior of real materials to simple but appropriate models, this way providing a deep understanding for the underlying mechanisms and an intuitive picture for many phenomena. In addition, the close interaction of theory and experiment stimulates the improvement and refinement of the methods in both areas, pioneering the grounds for more and more precise descriptions. Further pushing the limits of these mighty techniques will not only be a precondition for the success of fundamental research at the frontier between physics and chemistry, but also enables an advanced material design on computational grounds.:Contents List of abbreviations 1. Introduction 2. Methods 2.1. Electronic structure and magnetic models for real compounds 2.1.1. Describing a solid 2.1.2. Basic exchange and correlation functionals 2.1.3. Strong correlations 2.1.4. Band structure codes 2.1.5. Disorder and vacancies 2.1.6. Models on top of DFT 2.2. X-ray diffraction and x-ray absorption at extreme conditions 2.2.1. Diamond anvil cells 2.2.2. ID09 - XRD under pressure 2.2.3. ID24 - XAS and XMCD under pressure 3. Low dimensional magnets 3.1. Materials 3.1.1 AgCuVO4 - a model compound between two archetypes of Cu-O chains 3.1.2 Li2ZrCuO4 - in close vicinity to a quantum critical point 3.1.3 PbCuSO4(OH)2 -magnetic exchange ruled by H 3.1.4 CuCl2 and CuBr2 - flipping magnetic orbitals by crystal water 3.1.5 Na3Cu2SbO6 and Na2Cu2TeO6 - alternating chain systems 3.1.6 Cu2(PO3)2CH2 - magnetic vs. structural dimers 3.1.7 Cu2PO4OH - orbital order between dimers and chains 3.1.8 A2CuEO6 - an new family of spin 1/2 square lattice compounds 3.2. General trends and relations 3.2.1. Approximation for the treatment of strong correlation 3.2.2. Structural elements 4. Magnetic intermetallic compounds under extreme conditions 115 4.1. Itinerant magnets 4.1.1. YCo5 - a direct proof for a magneto elastic transition by XMCD 4.1.2. SrFe2As2 - symmetry-preserving lattice collapse 4.2. Localized magnets 4.2.1. EuPd3Bx - valence transition under doping and pressure 5. Summary and outlook A. Technical details B. Crystal Structures C. Supporting Material Bibliography List of Publications Acknowledgments