In this thesis, I present a microscopic theory of quantum circuits based on interacting electron spins in quantum dot molecules. We use the Linear Combination of Harmonic Orbitals-Configuration Interaction (LCHO-CI) formalism for microscopic calculations. We then derive effective Hubbard, t-J, and Heisenberg models. These models are used to predict the electronic, spin and transport properties of a triple quantum dot molecule (TQDM) as a function of topology, gate configuration, bias and magnetic field. With these theoretical tools and fully characterized TQDMs, we propose the following applications: 1. Voltage tunable qubit encoded in the chiral states of a half-filled TQDM. We show how to perform single qubit operations by pulsing voltages. We propose the "chirality-to-charge" conversion as the measurement scheme and demonstrate the robustness of the chirality-encoded qubit due to charge fluctuations. We derive an effective qubit-qubit Hamiltonian and demonstrate the two-qubit gate. This provides all the necessary operations for a quantum computer built with chirality-encoded qubits. 2. Berry's phase. We explore the prospect of geometric quantum computing with chirality-encoded qubit. We construct a Herzberg circuit in the voltage space and show the accumulation of Berry's phase. 3. Macroscopic quantum states on a semiconductor chip. We consider a linear chain of TQDMs, each with 4 electrons, obtained by nanostructuring a metallic gate in a field effect transistor. We theoretically show that the low energy spectrum of the chain maps onto that of a spin-1 chain. Hence, we show that macroscopic quantum states, protected by a Haldane gap from the continuum, emerge. In order to minimize decoherence of electron spin qubits, we consider using electron spins in the p orbitals of the valence band (valence holes) as qubits. We develop a theory of valence hole qubit within the 4-band k.p model. We show that static magnetic fields can be used to perform single qubit operations. We also show that the qubit-qubit interactions are sensitive to the geometry of a quantum dot network. For vertical qubit arrays, we predict that there exists an optimal qubit separation suitable for the voltage control of qubit-qubit interactions.

In this thesis, I present a microscopic theory of quantum circuits based on interacting electron spins in quantum dot molecules. We use the Linear Combination of Harmonic Orbitals-Configuration Interaction (LCHO-CI) formalism for microscopic calculations. We then derive effective Hubbard, t-J, and Heisenberg models. These models are used to predict the electronic, spin and transport properties of a triple quantum dot molecule (TQDM) as a function of topology, gate configuration, bias and magnetic field. With these theoretical tools and fully characterized TQDMs, we propose the following applications: 1. Voltage tunable qubit encoded in the chiral states of a half-filled TQDM. We show how to perform single qubit operations by pulsing voltages. We propose the "chirality-to-charge" conversion as the measurement scheme and demonstrate the robustness of the chirality-encoded qubit due to charge fluctuations. We derive an effective qubit-qubit Hamiltonian and demonstrate the two-qubit gate. This provides all the necessary operations for a quantum computer built with chirality-encoded qubits. 2. Berry's phase. We explore the prospect of geometric quantum computing with chirality-encoded qubit. We construct a Herzberg circuit in the voltage space and show the accumulation of Berry's phase. 3. Macroscopic quantum states on a semiconductor chip. We consider a linear chain of TQDMs, each with 4 electrons, obtained by nanostructuring a metallic gate in a field effect transistor. We theoretically show that the low energy spectrum of the chain maps onto that of a spin-1 chain. Hence, we show that macroscopic quantum states, protected by a Haldane gap from the continuum, emerge. In order to minimize decoherence of electron spin qubits, we consider using electron spins in the p orbitals of the valence band (valence holes) as qubits. We develop a theory of valence hole qubit within the 4-band k.p model. We show that static magnetic fields can be used to perform single qubit operations. We also show that the qubit-qubit interactions are sensitive to the geometry of a quantum dot network. For vertical qubit arrays, we predict that there exists an optimal qubit separation suitable for the voltage control of qubit-qubit interactions.

In this thesis, I present a microscopic theory of quantum circuits based on interacting electron spins in quantum dot molecules. We use the Linear Combination of Harmonic Orbitals-Configuration Interaction (LCHO-CI) formalism for microscopic calculations. We then derive effective Hubbard, t-J, and Heisenberg models. These models are used to predict the electronic, spin and transport properties of a triple quantum dot molecule (TQDM) as a function of topology, gate configuration, bias and magnetic field. With these theoretical tools and fully characterized TQDMs, we propose the following applications: 1. Voltage tunable qubit encoded in the chiral states of a half-filled TQDM. We show how to perform single qubit operations by pulsing voltages. We propose the "chirality-to-charge" conversion as the measurement scheme and demonstrate the robustness of the chirality-encoded qubit due to charge fluctuations. We derive an effective qubit-qubit Hamiltonian and demonstrate the two-qubit gate. This provides all the necessary operations for a quantum computer built with chirality-encoded qubits. 2. Berry's phase. We explore the prospect of geometric quantum computing with chirality-encoded qubit. We construct a Herzberg circuit in the voltage space and show the accumulation of Berry's phase. 3. Macroscopic quantum states on a semiconductor chip. We consider a linear chain of TQDMs, each with 4 electrons, obtained by nanostructuring a metallic gate in a field effect transistor. We theoretically show that the low energy spectrum of the chain maps onto that of a spin-1 chain. Hence, we show that macroscopic quantum states, protected by a Haldane gap from the continuum, emerge. In order to minimize decoherence of electron spin qubits, we consider using electron spins in the p orbitals of the valence band (valence holes) as qubits. We develop a theory of valence hole qubit within the 4-band k.p model. We show that static magnetic fields can be used to perform single qubit operations. We also show that the qubit-qubit interactions are sensitive to the geometry of a quantum dot network. For vertical qubit arrays, we predict that there exists an optimal qubit separation suitable for the voltage control of qubit-qubit interactions.

In this thesis, I present a microscopic theory of quantum circuits based on interacting electron spins in quantum dot molecules. We use the Linear Combination of Harmonic Orbitals-Configuration Interaction (LCHO-CI) formalism for microscopic calculations. We then derive effective Hubbard, t-J, and Heisenberg models. These models are used to predict the electronic, spin and transport properties of a triple quantum dot molecule (TQDM) as a function of topology, gate configuration, bias and magnetic field. With these theoretical tools and fully characterized TQDMs, we propose the following applications: 1. Voltage tunable qubit encoded in the chiral states of a half-filled TQDM. We show how to perform single qubit operations by pulsing voltages. We propose the "chirality-to-charge" conversion as the measurement scheme and demonstrate the robustness of the chirality-encoded qubit due to charge fluctuations. We derive an effective qubit-qubit Hamiltonian and demonstrate the two-qubit gate. This provides all the necessary operations for a quantum computer built with chirality-encoded qubits. 2. Berry's phase. We explore the prospect of geometric quantum computing with chirality-encoded qubit. We construct a Herzberg circuit in the voltage space and show the accumulation of Berry's phase. 3. Macroscopic quantum states on a semiconductor chip. We consider a linear chain of TQDMs, each with 4 electrons, obtained by nanostructuring a metallic gate in a field effect transistor. We theoretically show that the low energy spectrum of the chain maps onto that of a spin-1 chain. Hence, we show that macroscopic quantum states, protected by a Haldane gap from the continuum, emerge. In order to minimize decoherence of electron spin qubits, we consider using electron spins in the p orbitals of the valence band (valence holes) as qubits. We develop a theory of valence hole qubit within the 4-band k.p model. We show that static magnetic fields can be used to perform single qubit operations. We also show that the qubit-qubit interactions are sensitive to the geometry of a quantum dot network. For vertical qubit arrays, we predict that there exists an optimal qubit separation suitable for the voltage control of qubit-qubit interactions.

[pt] Nesta tese investigamos os efeitos das interações elétron- elétron nas propriedades de transporte nanosistemas. Em particular, estudamos sistemas constituídos por dois pontos quânticos conectados a dois contatos, em diferentes topologias. O principal interesse é estudar os efeitos do regime Kondo e da fase eletrônica na condutância. Na configuração onde os dois pontos são inseridos em cada braço de um anel atravessado por um fluxo magnético, denotada por PPL, calculamos as fases das correntes que circulam através de cada braço do anel. Estas fases são determinadas pelo efeito Aharonov-Bohm combinado com a inflência da interação de muitos corpos das cargas nos pontos. Este sistema apresenta ressonância Kondo para um número par de elétrons em concordância com os resultados experimentais1. Outro aspecto interessante da configuração PPL é que, mesmo na ausência de fluxo magnético, pode existir circulação de corrente no anel, dependendo dos parâmetros escolhidos. Consideramos outras duas topologias que envolvem dois pontos quânticos acoplados através de interação de tunelamento. Em uma delas, denotada PAL, os dois pontos estão alinhados com os contatos, e na outra, a configuração PPD, um ponto está inserido nos contatos entanto que o outro interage só com o primeiro. No limite de acoplamento fraco, estas duas configurações apresentam características bem distintas, no só na dependência da condutância com o potencial de porta mas também na correlação de spin dos pontos quânticos. Ambas configurações apresentam ressonância Kondo para um número par de elétrons de diferente natureza. Quando cada ponto está carregado com um elétron, no caso da configuração PAL, os spins dos pontos quânticos estão descorrelacionados enquanto que, na configuração PPD, os spins estão correlacionados ferromagneticamente. No limite do acoplamento forte as propriedades de transporte das dois configurações são similares. Os sistemas discutidos acima são representados por o Hamiltoniano de Anderson de duas impurezas acopladas, o qual é resolvido diagonalizando exatamente um aglomerado que é embebido no resto do sistema. Desta forma obtemos as propriedades de transporte a T = 0. Para estudar a dependência com a temperatura utilizamos o método da equação de movimento (EOM) no limite da repulsão Coulombiana infinita. Aplicamos este método ao caso da topologia PPD, obteniendo resultados para baixas temperaturas consistente com os obtidos com o método do aglomerado. / [en] In this thesis we investigate the effects of the eletron- eletron interaction on the transport properties of nanosystems. In particular, we study systems constituted by two quantum dots conected to leads, in different topologies. Our main interest is to study the effects of the Kondo regime and the electronic phase on the conductance. In the configuration where the two dots are inserted in each arm of a ring threaded by a magnetic flux, denoted by PPL, we calculate the phases of the currents going along each arm of the ring. These phases are determined by the Aharonov-Bohm effect combined with the dots many body charging effects. This system presents the Kondo phenomenon for an even number (two) of electrons in the dots, in agreement with experimental results1. An interesting aspect of PPL configuration is that, even in the absence of magnetic flux there can be a circulating current around the ring, depending on the system parameters. In the two other topologies we consider the two quantum dots coupled through tunneling interaction. In one of them, denoted by PAL, the two dots are aligned with the leads, and in the other, the PPD configuration, one dot is inserted into the leads while the other interacts only with the first. In the weak coupling limit these two configurations present quite different features, not only on the dependence of the conductance on the gate potencials applied to the dots, but also on the dots spin correlation. Both configurations present Kondo resonance for an even number electrons. In the PAL configuration the spins of the charged dots are uncorrelated, while in the PPD configuration they are ferromagnetically correlated. In the strong tunneling coupling limit the transport properties of two interacting dot configurations are very similar. The systems discussed above are represented by an Anderson two- impurity first-neighbor tight-binding Hamiltonian, that is solved by exactly diagonalizing a cluster that is embebed into the rest of the system. In this way we obtain only the properties of the system at T = 0. In order to study temperature dependence phenomena we use the equation of motion method (EOM) in the limit of infinite Coulomb repulsion. We apply it to the dots in the PPD topology. The results for low temperatures are consistent with hose obtained with the cluster method.

Nous étudions plusieurs problémes reliés aux propriétés de transport dans les systèmes corrélés. La thèse contient 3 parties distinctes, chacune d'entre elles décrivant un aspect particulier. Nous avons obtenu dans chacun des cas des résultats qui permettent une meilleure compréhension du transport. Nous étudions l'effet de la dissipation et d'une perturbation extérieure dépendant du temps sur le diagramme de phases d'un systèmes à N corps à température nulle et à température finie. En présence de perturbation dépendant du temps, la dissipation joue un rôle important dans l'évolution vers un état stable indépendant du temps. Nous utilisons le formalisme de Keldysh dans l'approximation adiabatique qui permet d'étudier le diagramme de phases du système en fonction de parameter et de la température. Dans la 2ième partie, nous étudions un concept important pour la physique des systèmes métalliques à plusieurs bandes, le concept d'hybridation, et la façon dont l'hybridation affecte la supraconductivité du métal. De façon générale, une hybridation dépendante ou non du vecteur d'onde k a tendance à détruire la supraconductivité. Nous montrons dans ce chapitre qu'une hybridation antisymétrique a l'effet inverse et renforce la supraconductivité. Nous montrons que si l'hybridation est antisymétrique, la supraconductivité a des propriétés non-triviales. Nous proposons que dans un tel système, il puisse exister des fermions de Majorana, même en l'absence de couplage spin-orbite. Le dernier chapitre de la thèse porte sur les effets du couplage spin-orbite sur le transport dans les nanostructures magnétiques. Dans les nanostructures, le couplage spin-orbite joue un rôle important en raison de la brisure de symmétrie à la surface ou aux interfaces. En particulier, nous étudions l'effet de l'interaction Dzyaloshinskii-Moriya (DM) sur le transport de spin dans un système tri-couche. Nous montrons qu'il existe une interaction DM entre les moments des couches et les électrons de conduction, et l'influence de cette interaction sur le transport est étudiée dans un modèle simplifié ou chaque couche est représentée par un point. / We study some important problems related to the transport properties of many body systems. It is divided in three parts, each one focusing in a specific topic. We obtain relevant results that improve our understanding of these systems. We investigate the effect of dissipation and time-dependent external sources, in the phase diagram of a many body system at zero and finite temperature. In the presence of time-dependent perturbations, dissipation is essential for the system to attain a steady, time independent state. In order to treat this time dependent problem, we use a Keldysh approach within an adiabatic approximation that allows us to study the phase diagram of this system as a function of the parameters of the system and temperature. We also discuss the nature of the quantum phase transitions of the system. Next, we study an important concept in the physics of metallic multi-band systems, that of hybridization, and how it affects the superconducting properties of a material. A constant or symmetric $k$-dependent hybridization in general act in detriment of superconductivity. We show here that when hybridization between orbitals in different sites assumes an anti-symmetric character having odd-parity it {it{enhances}} superconductivity. The antisymmetric hybridization in a problem study in this thesis (present in Chapter 3) allow us to propose a new system where it is possible to investigate Majorana fermions, even in absence of spin-orbit interactions. In the last part of this thesis we study the effect of spin-orbit coupling (SOC) on transport properties in magnetic nanostructures. In this system SOC plays an important role, because surfaces (or interfaces) introduce symmetry breaking which is a source of spin-orbit interaction. We study the role of Dzyaloshinshkii-Moriya (DM) interaction on spin-transport in a 3 layer system. We show that there is a DM interaction between magnetics ions in the layers and spin of conduction electrons. We study the influence of this DM interaction on transport within a simple model where each layer is represented by a point.

Nous étudions plusieurs problémes reliés aux propriétés de transport dans les systèmes corrélés. La thèse contient 3 parties distinctes, chacune d'entre elles décrivant un aspect particulier. Nous avons obtenu dans chacun des cas des résultats qui permettent une meilleure compréhension du transport. Nous étudions l'effet de la dissipation et d'une perturbation extérieure dépendant du temps sur le diagramme de phases d'un systèmes à N corps à température nulle et à température finie. En présence de perturbation dépendant du temps, la dissipation joue un rôle important dans l'évolution vers un état stable indépendant du temps. Nous utilisons le formalisme de Keldysh dans l'approximation adiabatique qui permet d'étudier le diagramme de phases du système en fonction de parameter et de la température. Dans la 2ième partie, nous étudions un concept important pour la physique des systèmes métalliques à plusieurs bandes, le concept d'hybridation, et la façon dont l'hybridation affecte la supraconductivité du métal. De façon générale, une hybridation dépendante ou non du vecteur d'onde k a tendance à détruire la supraconductivité. Nous montrons dans ce chapitre qu'une hybridation antisymétrique a l'effet inverse et renforce la supraconductivité. Nous montrons que si l'hybridation est antisymétrique, la supraconductivité a des propriétés non-triviales. Nous proposons que dans un tel système, il puisse exister des fermions de Majorana, même en l'absence de couplage spin-orbite. Le dernier chapitre de la thèse porte sur les effets du couplage spin-orbite sur le transport dans les nanostructures magnétiques. Dans les nanostructures, le couplage spin-orbite joue un rôle important en raison de la brisure de symmétrie à la surface ou aux interfaces. En particulier, nous étudions l'effet de l'interaction Dzyaloshinskii-Moriya (DM) sur le transport de spin dans un système tri-couche. Nous montrons qu'il existe une interaction DM entre les moments des couches et les électrons de conduction, et l'influence de cette interaction sur le transport est étudiée dans un modèle simplifié ou chaque couche est représentée par un point. / We study some important problems related to the transport properties of many body systems. It is divided in three parts, each one focusing in a specific topic. We obtain relevant results that improve our understanding of these systems. We investigate the effect of dissipation and time-dependent external sources, in the phase diagram of a many body system at zero and finite temperature. In the presence of time-dependent perturbations, dissipation is essential for the system to attain a steady, time independent state. In order to treat this time dependent problem, we use a Keldysh approach within an adiabatic approximation that allows us to study the phase diagram of this system as a function of the parameters of the system and temperature. We also discuss the nature of the quantum phase transitions of the system. Next, we study an important concept in the physics of metallic multi-band systems, that of hybridization, and how it affects the superconducting properties of a material. A constant or symmetric $k$-dependent hybridization in general act in detriment of superconductivity. We show here that when hybridization between orbitals in different sites assumes an anti-symmetric character having odd-parity it {it{enhances}} superconductivity. The antisymmetric hybridization in a problem study in this thesis (present in Chapter 3) allow us to propose a new system where it is possible to investigate Majorana fermions, even in absence of spin-orbit interactions. In the last part of this thesis we study the effect of spin-orbit coupling (SOC) on transport properties in magnetic nanostructures. In this system SOC plays an important role, because surfaces (or interfaces) introduce symmetry breaking which is a source of spin-orbit interaction. We study the role of Dzyaloshinshkii-Moriya (DM) interaction on spin-transport in a 3 layer system. We show that there is a DM interaction between magnetics ions in the layers and spin of conduction electrons. We study the influence of this DM interaction on transport within a simple model where each layer is represented by a point.

Orientador: Eduardo Miranda / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-16T08:19:56Z (GMT). No. of bitstreams: 1 Andrade_EricdeCastroe_D.pdf: 5537554 bytes, checksum: 1391d5fcc710b5e471f0814a4a6d484f (MD5) Previous issue date: 2010 / Resumo: Sistemas eletrônicos fortemente correlacionados desordenados possuem dois mecanismos básicos para a localização eletrônica e a subsequente destruição do estado metálico: o de Mott (causado pela interação elétron-elétron) e o de Anderson (causado pela desordem). Nesta tese, estudamos como estes mecanismos competem dentro da fase metálica e também como afetam o comportamento crítico do sistema, empregando uma generalização para o caso desordenado do cenário de Brinkman-Rice para a transição de Mott. Investigamos os efeitos de desordem fraca e moderada sobre a transição metal-isolante de Mott a T = 0 em duas dimensões. Para desordem sucientemente baixa, a transição mantém sua característica do tipo Mott, na qual temos os pesos de quasipartícula Zi indo a zero na transição e uma forte blindagem da desordem na região crítica. Em contraste com o comportamento encontrado para d = 8 , no nosso caso as flutuações espaciais dos pesos de quasipartícula são fortemente amplificadas próximo à transição de Mott de tal forma que eles adquirem uma distribuição do tipo lei de potência P (Z) ~ Z a-1 ,com a --> 0 na transição. Tal comportamento altera completamente as características desta transição com relação ao caso limpo, e é um indício robusto da emergência de uma fase de Griffiths eletrônica precedendo a transição metal-isolante de Mott, com uma fenomenologia surpreendentemente similar àquela do "ponto fixo de desordem infinita" encontrada em magnetos quânticos. Uma consequência imediata dessas novas características introduzidas pela desordem é que estados eletrônicos próximos à superfície de Fermi tornam-se mais homogêneos na região crítica, ao passo que estados com maiores energias têm o comportamento oposto: eles apresentam uma grande inomogeneidade precisamente nas vizinhanças da transição de Mott. Sugerimos que uma desordem efetiva dependente da interação é uma característica comum a todos os sistemas de Mott desordenados. Estudamos também como os efeitos bem conhecidos das oscilações de longo alcance de Friedel são afetados por fortes correlações eletrônicas. Primeiramente, mostramos que sua amplitude e alcance são consideravelmente suprimidos em líquidos de Fermi fortemente renormalizados. Posteriormente, investigamos o papel dos espalhamentos elásticos e inelásticos na presença dessas oscilações. Em geral, nossos resultados analíticos mostram que um papel proeminente das oscilações de Friedel é relegado a sistemas fracamente interagentes. Abordamos, por m, os efeitos das interações sobre o isolante de Anderson em uma dimensão. Construímos a função de escala ß (g) e mostramos que a escala de "crossover" g *, que marca a transição entre o regime ôhmico e o localizado da condutância, é renormalizada pelas interações. Como consequência, embora não haja a emergência de estados verdadeiramente estendidos, o regime ôhmico de g estende-se agora por uma região consideravelmente maior do espaço de parâmetros. / Abstract: Disordered strongly correlated electronic systems have two basic routes towards localization underlying the destruction of the metallic state: the Mott route (driven by electron-electron interaction) and the Anderson route (driven by disorder). In this thesis, we study how these two mechanisms compete in the metallic phase, and also how they change the critical behavior of the system, within a generalization to the disordered case of the Brinkman-Rice scenario for the Mott transition. We investigate the effects of weak to moderate disorder on the Mott metal-insulator transition at T = 0 in two dimensions. For sufficiently weak disorder, the transition retains the Mott character, as signaled by the vanishing of the local quasiparticle weights Zi and strong disorder screening at criticality. In contrast to the behavior in d = 8, here the local spatial fluctuations of quasiparticle parameters are strongly enhanced in the critical regime, with a distribution function P(Z) ~ Z a-1 and a --> 0 at the transition. This behavior indicates the robust emergence of an electronic Griffiths phase preceding the MIT, in a fashion surprisingly reminiscent of the " Infinite Randomness Fixed Point" scenario for disordered quantum magnets. As an immediate consequence of these new features introduced by disorder, we have that the electronic states close to the Fermi energy become more spatially homogeneous in the critical region, whereas the higher energy states show the opposite behavior: they display enhanced spatial inhomogeneity precisely in the close vicinity to the Mott transition. We suggest that such energy-resolved disorder screening is a generic property of disordered Mott systems. We also study how well-known effects of the long-ranged Friedel oscillations are affected by strong electronic correlations. We first show that their range and amplitude are signifficantly suppressed in strongly renormalized Fermi liquids. We then investigate the interplay of elastic and inelastic scattering in the presence of these oscillations. In the singular case of two-dimensional systems, we show how the anomalous ballistic scattering rate is conned to a very restricted temperature range even for moderate correlations. In general, our analytical results indicate that a prominent role of Friedel oscillations is relegated to weakly interacting systems. Finally, we discuss the effects of correlations on the Anderson insulator in one dimension. We construct the scaling function ß(g) and we show that the crossover scaling g*, which marks the transition between the ohmic and the localized regimes of the conductance, is renormalized by the interactions. As a consequence, we show that, although truly extend states do not emerge, the ohmic regime covers now a considerably larger region in the parameter space. / Doutorado / Física da Matéria Condensada / Doutor em Ciências

Die Arbeit befaßt sich mit der Messung und Analyse der spezifischen Wärme verschiedener stark korrelierter Elektronensysteme bei tiefen Temperaturen und hohen Magnetfeldern. Zunächst wird der im Rahmen dieser Arbeit verwendete, auf der Meßmethode der thermischen Relaxation beruhende Aufbau des Kalorimeters (Einsatzbereich 0.05K<T<4K und 0<B<12T) ausführlich erläutert. Danach werden die Ergebnisse von Messungen an den drei Schwere-Fermionen-Verbindungen CeCu2Si2, CeNi2Ge2 und YbRh2Si2 dargelegt. Wenngleich alle drei Systeme bei tiefen Temperaturen durch den für Schwere-Fermionen-Systeme charakteristischen, stark erhöhten elektronischen Beitrag zur spezifischen Wärme gekennzeichnet sind zeigen sich deutliche Unterschiede im beobachteten Grundzustandsverhalten. An CeCu2Si2 wird die für T<1K auftretende Konkurrenz zwischen einem supraleitenden und einem magnetischen Grundzustand ausführlich studiert. In YbRh2Si2 zeigt sich bei einer für 4f-Systeme bemerkenswert tiefen Temperatur von ca. 70mK ein Übergang in eine magnetische Phase, während der Grundzustand von CeNi2Ge2 wegen stark ausgeprägter Probenabhängigkeiten immer noch kontrovers diskutiert wird. Des weiteren zeigen alle drei Verbindungen deutliche Abweichungen vom Verhalten einer Fermi-Flüssigkeit. Die Theorie der Fermi-Flüssigkeit hat sich für metallische Verbindungen als sehr erfolgreich auch bei der Beschreibung des Verhaltens eines Systems aus stark wechselwirkenden Ladungsträgern erwiesen. Warum diese Theorie auf die untersuchten Verbindungen nicht anwendbar zu sein scheint, wird im Rahmen moderner Modellvorstellungen wie z. B. der Nähe zu einem quantenkritischen Punkt diskutiert. Die an Sr2RuO4, dem ersten Kupfer-freien Perowskit Supraleiter, durchgeführten Messungen der spezifischen Wärme dokumentieren das Auftreten von zwei Zusatzbeiträgen für T<Tc, die eine Interpretation der spezifischen Wärme des supraleitenden Zustands von Sr2RuO4 im Hinblick auf die Topologie des Ordnungsparameters deutlich erschweren.

This thesis consists of six chapters. The first chapter gives an introduction to the field of low-dimensional magnetic and electronic systems and relevant numerical techniques. The recent developments in molecular magnets are highlighted. The numerical techniques are reviewed along with their advantages and disadvantages from the present perspective. Study of entanglement of a system can give a great insight into the system. At the last part of this chapter a general overview is given regarding entanglement, its measures and its significance in studying many-body systems. Chapter 2 deals with the technique that has been developed by us for the full symmetry adaptation of non-relativistic Hamiltonians. It is advantageous both computationally and physically/chemically to exploit both spin and spatial symmetries of a system. It has been a long-standing problem to target a state which has definite total spin and also belongs to a definite irreducible representation of a point group, particularly for non-Abelian point groups. A very general technique is discussed in this chapter which is a hybrid method based on valence-bond basis and the basis of the z-component of the total spin. This technique is not only applicable to a system with arbitrary site spins and belonging to any point group symmetry, it is also quite easy to implement computationally. To demonstrate the power of the method, it is applied to the molecular magnetic system, Cu6Fe8, with cubic symmetry. In chapter 3, the extension of the previous hybrid technique to electronic systems is discussed. The power of the method is illustrated by applying it to a model icosahedral half-filled electronic system. This model spans a huge Hilbert space (dimension 1,778,966) and is in the largest non-Abelian point group. All the eigenstates of the model are obtained using our technique. Chapter 4 deals with the thermodynamic properties of an important class of single-chain magnets (SCMs). This class of SCMs has alternate isotropic spin-1/2 units and anisotropic high spin units with the anisotropy axes being non-collinear. Here anisotropy is assumed to be large and negative, as a result, anisotropic units behave like canted spins at low temperatures; but even then simple Ising-type model does not capture the essential physics of the system due to quantum mechanical nature of the isotropic units. A transfer matrix (TM) method is developed to study statistical behavior of this class of SCMs. For the first time, it is also discussed in detail that how weak inter-chain interactions can be treated by a TM method. The finite size effect is also discussed which becomes important for low temperature dynamics. This technique is applied to a real helical chain magnet, which has been studied experimentally. In the fifth chapter a bipartite entanglement entropy of finite systems is studied using exact diagonalization techniques to examine how the entanglement changes in the presence of long-range interactions. The PariserParrPople model with long-range interactions is used for this purpose and corresponding results are com-pared with those for the Hubbard and Heisenberg models with short-range interactions. This study helps understand why the density matrix renormalization group (DMRG) technique is so successful even in the presence of long-range interactions in the PPP model. It is also investigated if the symmetry properties of a state vector have any significance in relation to its entanglement. Finally, an interesting observation is made on the entanglement profiles of different states, across the full energy spectrum, in comparison with the corresponding profile of the density of states. The entanglement can be localized between two noncomplementary parts of a many-body system by performing local measurements on the rest of the system. This localized entanglement (LE) depends on the chosen basis set of measurement (BSM). In this chapter six, an optimality condition for the LE is derived, which would be helpful in finding optimal values of the LE, besides, can also be of use in studying mixed states of a general bipartite system. A canonical way of localizing entanglement is further discussed, where the BSM is not chosen arbitrarily, rather, is fully determined by the properties of a system. The LE obtained in this way, called the localized entanglement by canonical measurement (LECM), is not only easy to calculate practically, it provides a nice way to define the entanglement length. For spin-1/2 systems, the LECM is shown to be optimal in some important cases. At the end of this chapter, some numerical results are presented for j1 −j2 spin model to demonstrate how the LECM behaves.