<p>This thesis is divided into two parts. In the first part we study thermodynamics of the two-dimensional Heisenberg ferromagnet with dipolar interaction. This interaction breaks the conditions of the Mermin-Wagner theorem, resulting in a finite transition temperature. Our calculations are done within the framework of the self-consistent spin-wave theory (SSWT), which is modified in order to include the dipolar interaction. Both quantum and classical versions of the Heisenberg model are considered.</p><p>The second part of the thesis investigates the chemical bonding in solids from the first principles calculations. A new chemical bonding indicator called balanced crystal orbital overlap population (BCOOP) is developed. BCOOP is less basis set dependent than the earlier indicators and it can be used with full-potential density-functional theory (DFT) codes. We apply BCOOP formalism to the chemical bonding in the high-T_c superconductor MgB2 and the theoretically predicted MAX phase Nb3SiC2. We also study how the chemical bonding results in a repulsive hydrogen–hydrogen interaction in metal hydrides. The role of this interaction in the structural phase transition in Ti3SnHx is investigated.</p>

This thesis is divided into two parts. In the first part we study thermodynamics of the two-dimensional Heisenberg ferromagnet with dipolar interaction. This interaction breaks the conditions of the Mermin-Wagner theorem, resulting in a finite transition temperature. Our calculations are done within the framework of the self-consistent spin-wave theory (SSWT), which is modified in order to include the dipolar interaction. Both quantum and classical versions of the Heisenberg model are considered. The second part of the thesis investigates the chemical bonding in solids from the first principles calculations. A new chemical bonding indicator called balanced crystal orbital overlap population (BCOOP) is developed. BCOOP is less basis set dependent than the earlier indicators and it can be used with full-potential density-functional theory (DFT) codes. We apply BCOOP formalism to the chemical bonding in the high-T_c superconductor MgB2 and the theoretically predicted MAX phase Nb3SiC2. We also study how the chemical bonding results in a repulsive hydrogen–hydrogen interaction in metal hydrides. The role of this interaction in the structural phase transition in Ti3SnHx is investigated.

In this work a numerical approach for the determination of the energy spectra and the calculation of thermodynamic properties of magnetic molecules is presented. The work is focused on the treatment of spin systems which exhibit point-group symmetries. Ring-like and archimedean-type structures are discussed as prominent examples. In each case the underlying spin quantum system is modeled by an isotropic Heisenberg Hamiltonian. Its energy spectrum is calculated either by numerical exact diagonalization or by an approximate diagonalization method introduced here. In order to implement full spin-rotational symmetry the numerical approach at hand is based on the use of irreducible tensor operators. Furthermore, it is shown how an unrestricted use of point-group symmetries in combination with the use of irreducible tensor operators leads to a reduction of the dimensionalities as well as to additional information about the physics of the systems. By exemplarily demonstrating how the theoretical foundations of the irreducible tensor operator technique can be realized within small spin systems the technical aspect of this work is covered. These considerations form the basis of the computational realization that was implemented and used in order to get insight into the investigated systems.

In this work we studied magnetic properties of molecular magnets of the new heteropolyanion {Cu20}, dodecanuclear cluster {Ni12}, and the heterometallic {Cr7M} wheels, in which one of the CrIII ions of Cr8 has been replaced by a Fe, Cu, Zn, Ni, ion with this extra-spin acts as local probe for the spin dynamics.Such systems have been synthesized recently and they are well described using the Heisenberg spin Hamiltonian with a Zeeman term of an applied magnetic field along the z-axis. Using the numerical exact diagonalization method, we have calculated the energy spectrum and the eigenstates for different compounds,and we have used them for reexamining the available experimental susceptibility data to determine the values of exchange parameters.We have studied the thermodynamic properties such magnetization, susceptibility, heat-capacity. At low temperature regions molecular magnets act as individual quantum nanomagnets and can display super-paramagnetic phenomena like macroscopic quantum tunneling, ground state degeneracy, level-crossing. A crucial issue for understanding these phenomena is the coupling between magnetic molecular levels and the environment such as nuclear spins. We have modeled the behavior of the proton spin lattice relaxation rate as a function of applied magnetic field for low temperatures as it is measured in Nuclear Magnetic Resonance (NMR) experiments.

Le domaine des problèmes quantiques à N-corps à l'équilibre et hors d'équilibre sont des sujets majeurs de la Physique et de la Physique de la matière condensée en particulier. Les propriétés d'équilibre de nombreux systèmes unidimensionnels en interaction sont bien comprises d'un point de vue théorique, des chaînes de spins aux théories quantiques des champs dans le continue. Ces progrès ont été rendus possibles par le développement de nombreuses techniques puissantes, comme, par exemple, l'ansatz de Bethe, le groupe de renormalisation, la bosonisation, les états produits de matrices ou la théorie des champs invariante conforme. Même si les propriétés à l'équilibre de nombreux modèles soient connues, ceci n'est en général pas suffisant pour décrire leurs comportements hors d'équilibre, et ces derniers restent moins explorés et beaucoup moins bien compris. Les modèles d'impuretés quantiques représentent certains des modèles à N-corps les plus simples. Mais malgré leur apparente simplicité ils peuvent capturer plusieurs phénomènes expérimentaux importants, de l'effet Kondo dans les métaux aux propriétés de transports dans les nanostructures, comme les points quantiques. Dans ce travail nous considérons un modèle d'impureté appelé "modèle de niveau résonnant en interaction" (IRLM). Ce modèle décrit des fermions sans spin se propageant dans deux fils semi-infinis qui sont couplés à un niveau résonant -- appelé point ou impureté quantique -- via un terme de saut et une répulsion Coulombienne. Nous nous intéressons aux situations hors d'équilibre où un courant de particules s'écoule à travers le point quantique, et étudions les propriétés de transport telles que le courant stationnaire (en fonction du voltage), la conductance différentielle, le courant réfléchi, le bruit du courant ou encore l'entropie d'intrication. Nous réalisons des simulations numériques de la dynamique du modèle avec la méthode du groupe de renormalisation de la matrice densité dépendent du temps (tDMRG), qui est basée sur une description des fonctions d'onde en terme d'états produits de matrices. Nous obtenons des résultats de grande précision concernant les courbes courant-voltage ou bruit-voltage de l'IRLM, dans un grand domaine de paramètres du modèle (voltage, force de l'interaction, amplitude de saut vers le dot, etc.). Ces résultats numériques sont analysés à la lumière de résultats exacts de théorie des champs hors d'équilibre qui ont été obtenus pour un modèle similaire à l'IRLM, le modèle de Sine-Gordon avec bord (BSG). Cette analyse est en particulier basée sur l'identification d'une échelle d'énergie Kondo et d'exposants décrivant les régimes de petit et grand voltage. Aux deux points particuliers où les modèles sont connus comme étant équivalents, nos résultats sont en accord parfait avec la solution exacte. En dehors de ces deux points particuliers nous trouvons que les courbes de transport de l'IRLM et du modèle BSG demeurent très proches, ce qui était inattendu et qui reste dans une certaine mesure inexpliqué. / The fields of in- and out-of-equilibrium quantum many-body systems are major topics in Physics, and in condensed-matter Physics in particular. The equilibrium properties of one-dimensional problems are well studied and understood theoretically for a vast amount of interacting models, from lattice spin chains to quantum fields in a continuum. This progress was allowed by the development of diverse powerful techniques, for instance, Bethe ansatz, renormalization group, bosonization, matrix product states and conformal field theory. Although the equilibrium characteristics of many models are known, this is in general not enough to describe their non-equilibrium behaviors, the latter often remain less explored and much less understood. Quantum impurity models represent some of the simplest many-body problems. But despite their apparent simplicity, they can capture several important experimental phenomena, from the Kondo effect in metals to transport in nanostructures such as point contacts or quantum dots. In this thesis consider a classic impurity model - the interacting resonant level model (IRLM). The model describes spinless fermions in two semi-infinite leads that are coupled to a resonant level -- called quantum dot or impurity -- via weak tunneling and Coulomb repulsion. We are interested in out-of-equilibrium situations where some particle current flows through the dot, and study transport characteristics like the steady current (versus voltage), differential conductance, backscattered current, current noise or the entanglement entropy. We perform extensive state-of-the-art computer simulations of model dynamics with the time-dependent density renormalization group method (tDMRG) which is based on a matrix product state description of the wave functions. We obtain highly accurate results concerning the current-voltage and noise-voltage curves of the IRLM in a wide range parameter of the model (voltage bias, interaction strength, tunneling amplitude to the dot, etc.).These numerical results are analyzed in the light of some exact out-of-equilibrium field-theory results that have been obtained for a model similar to the IRLM, the boundary sine-Gordon model (BSG).This analysis is in particular based on identifying an emerging Kondo energy scale and relevant exponents describing the high- and low- voltage regimes. At the two specific points where the models are known to be equivalent our results agree perfectly with the exact solution. Away from these two points, we find that, within the precision of our simulations, the transport curves of the IRLM and BSG remain very similar, which was not expected and which remains somewhat unexplained.