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ilustraciones, graficas El presente trabajo estudia y extiende, mediante argumentos de universalidad, el comportamiento térmico dentro del régimen Kondo, de las distintas propiedades termoeléctricas tales como: La termopotencia, la conductancia eléctrica y la conductancia térmica, dentro de nanoestructuras semiconductoras comprimidas. Aduciendo, a la fuerte evidencia tanto experimental como teórica de condiciones de universalidad para la conductancia eléctrica zero − bias (sin potencial externo aplicado), en función de la temperatura normalizada T∗ = T/TK, con TK actuando como la temperatura de Kondo. Estudiamos, por medio del modelo de impureza de Anderson SIAM, un sistema idealizado compuesto por un punto cuántico inmerso dentro un canal de conducción balístico (hilos cuánticos). Para este sistema, se establece un mapeo lineal sobre el cual, se pueden expresar los coeficientes de transporte termoeléctrico, en términos de la condición (universal) simétrica partícula-hueco, junto a un cambio fase δ producto de los procesos de dispersión cuánticos. Asimismo, bajo el grupo de renormalización numérica (NRG), se calculan los coeficientes termoeléctricos para este sistema, permitiendo así, ilustrar tanto la física implícita en estos procesos, como la validez del mapeo lineal, dentro de un variado rango de temperaturas. De igual modo, se aplicaron los resultados obtenidos, para los coeficientes termoeléctricos en su forma universal, sobre algunos resultados experimentales recientes, asociados a la conductancia eléctrica y el termo-voltaje Vgate dentro de un rango limitado de temperaturas en el régimen Kondo. Logrando con esto, calcular todas las propiedades termoeléctricas derivadas de los mismos, seguido de la obtención, de algunas expresiones analíticas simples, que pueden ser empleadas para predecir, validar y/o ajustar resultados experimentales. Sin embargo, debido a la ausencia de mediciones experimentales, sobre las otras propiedades termoeléctricas dentro de un rango variado de temperaturas, no fue posible examinar la validez de los resultados para las mismas. Por otro lado, empleando las relaciones universales obtenidas para los coeficientes de transporte termoeléctrico (Onsager), junto al parámetro de Mahan-Sofo. Se logra deducir una expresión tal que permite, obtener condiciones que maximizan la figura térmica de mérito multiplicada por la temperatura ZT en función del cambio de fase δ implícito, dentro del régimen Kondo. Así, al evaluar esta expresión sobre el sistema de un único punto cúantico inmerso entre dos hilos cuánticos, se encuentra que, bajo estas condiciones, es físicamente imposible obtener un cambio de fase, que permita maximizar la eficiencia térmica de este tipo de sistemas. De esta forma, se estudia mediante el método de aproximación atómica, un sistema “mejorado” compuesto por dos puntos cuánticos acoplados no interactuantes entre si, pero con fuerte correlación electrónica en cada punto cuántico. En este sistema, variando la energía del primer punto cuántico (el Vgate en sistemas experimentales), mientras se mantiene el segundo punto cuántico en la condición simétrica (simetría-electrón-hueco), se logra encontrar condiciones que replican el cambio de fase δ necesario para optimizar la figura térmica de mérito ZT y por ende, la eficiencia termoeléctrica del sistema. (Texto tomado de la fuente) The present work studies and extends, by universality arguments, the thermal behavior on the Kondo regime, for the different thermoelectric properties like: Thermopower, electrical conductance and thermal conductance. Within compressed semiconductor nanostructures. Adducing, to the strong experimental and theoretical evidence of universality conditions, for the electrical conductance zero − bias (no external potential applied), as a function of the normalized temperature T∗ =T/TK, where TK is the Kondo temperature. Studying, by the single impurity model SIAM, on an idealized system composed of a quantum dot enbedded in a ballistic conduction channel (quantum wires). For this system, we establish a linear mapping for the thermoelectric transport coefficients, allowing expressed in terms of the universal symmetric particle-hole condition, together with a phase shift δ product of the quantum scattering process. Likewise, under the numerical renormalization group (NRG), the thermoelectric coefficients for this system are calculated, thus allowing to illustrate both the physics implicit in these process, as well as the validity of the linear mapping, within a wide range of temperatures. On the same way, applying the thermoelectric coefficients in their universal form, on some recent experimental results, associated with the electrical conductance and the thermo-voltage Vgate on a limited temperature range in the Kondo regime. Achieving with this, calculate all the thermoelectric properties derived from them, followed by some simple analytical fit expressions, which can be used to predict, validate and/or adjust experimental results. However, due to the absence of experimental measurements for others thermoelectric properties within widdly range of temperatures, it was not possible examine the validity of the results for them. By other way, using the universal relationships obtained for the thermoelectric transport coefficients (Onsager), together with the Mahan-Sofo parameter. It is possible to deduce an expression such that it allows obtaining conditions that maximize the thermal figure of merit multiplied by the temperature ZT as a function of the implicit phase shift δ. Thus, when we evaluatate this expression on the system of a single quantum dot immersed between two quantum wires, in the Kondo regime. We found that, under these conditions, it is physically impossible to obtain a phase shift that allows maximizing the thermal efficiency for this type of system. Then, using the atomic approximation method, on a “tuned” system composed of two coupled quantum dots whitout interdot correlation, but strongly correlated in each quantum dot. On which, varying the energy level on the first quantum dot (the Vgate in experimental systems), while maintaining the second quantum dot in the symmetric electron-hole condition. It’s possible find, conditions that replicate the phase shift δ necessary to optimize the thermal figure of merit ZT and therefore, the thermodynamic efficiency of these type systems Maestría Magíster en Ciencias - Física Sistemas nanoestructurados

Ce0.5La0.5Ni9Ge4 compound shows both Fermi and non-Fermi Liquid behaviour. Cerium is considered a magnetic atom and literature usually shows its electronic valence as Ce 3 + with j = 5 / 2 total angular momentum. In this paper we use two-channel Anderson Model and also density functional theory (DFT) to address this information. The Numerical Renormalization Group (NRG) is used to diagonalize this model and to obtain electronic specific heat versus temperature curves, from which entropy and degrees of freedom of the Anderson Model are taken. Both NRG and DFT indicate that Cerium atom must have Ce 1 + electronic valence and j = 9 / 2 total angular momentum.

We systematically study a numerical procedure that reveals the asymptotically self-similar dynamics of solutions of partial differential equations (PDEs). This procedure, based on the renormalizati...

This thesis investigates (i) the correlation effects in the emergence of bound states in the continuum (BIC); and (ii) non-equilibrium effects of the asymmetric two-channel Kondo problem. BICs are discrete states embedded in the continuum. They have localized wave-function and are originated by the quantum interference effects. In the first project of this thesis, we investigate the correlation effects in the emergence of a BIC in a two identical quantum dot device coupled to a quantum wire. This device was modeled by the two-impurity Anderson Hamiltonian and diagonalized via the Numerical Renormalization Group method. Given the symmetry between the quantum dots, the system was projected on the bonding and antibonding orbital representation resulting from the symmetric and antisymmetric combinations of the quantum dots, respectively. In the non-interacting regime, the antibonding orbital is a Friedrich-Wintgen BIC. As the Coulomb interaction grows, the antibonding orbital is indirectly coupled to the continuum via spin-spin and isospin-isospin interactions with the bonding orbital. In addition, at zero-temperature, the Coulomb interaction triggers a quantum phase transition between a magnetic and a non-magnetic phase. The magnetic phase is associated to the emergence of a bound spin state in the continuum (spin-BIC). The phase transition results from competition between a singlet isospin state, formed by the isospin-isospin interaction, and a triplet spin state, formed by the spin-spin interaction, between the two orbitals. The two phases are due to the conservation of the spin of the antibonding orbital. At low temperature, the spin-BIC interacts ferromagnetically with the conduction band, and the interaction renormalizes to zero as T → 0. In the second project of this thesis, motivated by a recent experiment [Z. Iftikhar et al., Nature 526, 233 (2015)], we investigate the transport properties of a macroscopic metallic island coupled to two leads. In the low-energy regime, only two charging states of the island are energetically accessible, which mimic a pseudospin-1/2. The charge fluctuations on the island emulate a spin-flip mechanism. Therefore, the low- energy physics of this device is well described by the anisotropic two-channel Kondo model. To explore the non-linear electronic transport, the system is driven out of equilibrium by the sudden application of a bias voltage between the leads. Time-dependent Density Matrix Renormalization Group computations follow the time evolution of the electrical current for times longer than the transient regime, although not long enough to reach the steady state. In the symmetric-coupling regime, the time-dependent current and differential conductance measurements show the universal behavior of the two-channel Kondo effect. In this limit, the differential conductance scales with the square root of the Kondo temperature and vary with the square of the bias voltage. In the presence of asymmetry, the transient behavior can be explained via energy-time uncertainty principle. As a function of the bias voltage, the conductance displays the expected crossover from non-Fermi liquid to Fermi-liquid behavior. Esta tese investiga (i) os efeitos de forte correlação eletrônica na emergência de estados ligado no contínuo (BICs - bound states in the continuum); e (ii) os efeitos de não- equilíbrio no problema Kondo anisotrópico de dois canais. BICs são estados discretos embebidos no contínuo. Eles possuem função de onda localizada e são originados por efeito de interferência quântica. No primeiro projeto desta tese, investigamos os efeitos de correlação eletrônica na emergência de um BIC em um dispositivo de dois pontos quânticos idênticos acoplados a um fio quântico. Esse dispositivo foi modelado pelo Hamiltoniano de Anderson de duas impurezas e diagonalizado pelo grupo de Renormalização Numérico. Dada a simetria entre os pontos quânticos, o sistema foi projetado na representação de orbitais ligante e antiligante obtida pela combinação simétrica e antissimétrica dos pontos quânticos, respectivamente. No regime não interagente, o orbital antiligante é um BIC de Friedrich-Wintgen. Conforme a interação de Coulomb cresce, o orbital antiligante se acopla indiretamente com o contínuo, via interação de spin-spin e isospin-isospin, com o orbital ligante. Além disso, à temperatura zero, o aumento da interação de Coulomb desencadeia uma transição de fase quântica entre uma fase magnética e outra não magnética, sendo o magnetismo resultado da emergência de um estado ligado no contínuo de um único spin (spin-BIC). A transição de fase se deve a competição entre um estado singleto de isospin, formado pela interação isospin-isospin, e um estado tripleto de spin, formado pela interação spin-spin, entre os orbitais. As duas fases refletem a conservação do spin do orbital antiligante. No limite de baixas temperaturas, o spin-BIC interage ferromagneticamente com a banda de condução, mas a interação é renormalizada para zero para T → 0. No segundo projeto, motivado por um experimento recente [Z. Iftikhar et al., Nature 526, 233 (2015)], estudamos o transporte eletrônico em uma ilha metálica macroscópica acoplada a dois terminais. No regime de baixas temperaturas, dois estados de carga da ilha são energeticamente acessíveis, que emulam um pseudo spin-1/2. A flutuação de carga induzida pela transferência de elétrons entre os terminais e a ilha simula um mecanismo de spin-flip. A física de baixas energias desse dispositivo é bem descrita pelo modelo Kondo anisotrópico de dois canais. Para explorar o transporte eletrônico não-linear, o sistema é tirado do equilíbrio pela aplicação repentina de uma diferença de potencial entre os terminais. Cálculos de Grupo de Renormalização da Matriz da Densidade permitem atingir tempos longos o suficiente para descrever o regime de transiente, mas não longo o suficiente para atingir o estado estacionário. Medidas de corrente e condutância diferencial dependente do tempo revelaram um comportamento universal do efeito Kondo de dois canais. A condutância diferencial escala com a raiz quadrada da temperatura Kondo e varia com o quadrado da diferença de potencial aplicada. Na presença de assimetria de carga, o regime transiente pode ser explicado pela relação de incerteza energia-tempo. A condutância diferencial em função da diferença de potencial mostra um crossover de uma fase de não-líquido de Fermi para uma de líquido de Fermi.

We investigate the effect of local geometry and environment on the electronic spin of nitric oxide (NO) on Au(110)-(1×2) using scanning tunneling microscopy/spectroscopy, density functional theory, and numerical renormalization group calculations. The molecules adsorb on the bridge or on-top sites, and the Kondo resonance is observed only for the latter. This indicates that the local geometry influences the spin state of NO on the surface. The Kondo resonance is accompanied by enhanced satellite peaks due to the interplay with vibrational excitation. In addition, we find that the Kondo resonance appears as a peak or a dip, depending on the local environment of the molecule. The calculations reveal that the NO/Au(110) system is represented by a two-orbital Anderson model, where the 2π∗ orbitals compete for the unpaired electron to host the Kondo resonance. We propose that a subtle interaction between the NO molecules may play a critical role in determining the host of Kondo resonance and, consequently, the spectral shape.

Local three- and four-point correlators yield important insight into strongly correlated systems and have many applications. However, the nonperturbative, accurate computation of multipoint correlators is challenging, particularly in the real-frequency domain for systems at low temperatures. In the accompanying paper, we introduce generalized spectral representations for multipoint correlators. Here, we develop a numerical renormalization group (NRG) approach, capable of efficiently evaluating these spectral representations, to compute local three- and four-point correlators of quantum impurity models. The key objects in our scheme are partial spectral functions, encoding the system's dynamical information. Their computation via NRG allows us to simultaneously resolve various multiparticle excitations down to the lowest energies. By subsequently convolving the partial spectral functions with appropriate kernels, we obtain multipoint correlators in the imaginary-frequency Matsubara, the real-frequency zero-temperature, and the real-frequency Keldysh formalisms. We present exemplary results for the connected four-point correlators of the Anderson impurity model, and for resonant inelastic x-ray scattering (RIXS) spectra of related impurity models. Our method can treat temperatures and frequencies -- imaginary or real -- of all magnitudes, from large to arbitrarily small ones., Comment: See also the jointly published paper [F. B. Kugler, S.-S. B. Lee, and J. von Delft, Phys. Rev. X 11, 041006 (2021); arXiv:2101.00707]

Wir pr��sentieren einen Ansatz zur Behandlung von Quantenst��rstellensystemen, der die numerische Renormierungsgruppe (NRG) zu einem offenen-Quantensystem-Formalismus erweitert. Das kontinuierliche Leitungsband wird in eine beliebige Wilsonkette und einen Satz von Reservoirs aufgeteilt, ohne die lokale Badhybridisierungsfunktion zu beeinflussen. An jedes Kettenglied wird jeweils ein Reservoir ��ber den Bloch-Redfield Formalismus (BRF) angekoppelt, der eine Born-Markov-N��herung (BMN) impliziert. Dieser offene-Wilsonketten-Formalismus (OWF) garantiert eine echte Thermalisierung f��r lokale nicht-Gleichgewichtsdynamik, sowie eine endliche Lebenszeit f��r lokale Gleichgewichtsspektralfunktionen. Der Ansatz reproduziert die von der NRG vorhergesagten Gleichgewichtswerte f��r t ��� ��� und die korrekten Relaxationsraten f��r das Resonanzlevel-Modell. Durch Verl��ngerung der Wilsonkette wird die Genauigkeit der BMN, speziell f��r die Kurzzeitdynamik, erh��ht. Die Formierung der Hubbardh��gel und der Kondoresonanz k��nnen f��r das Einzelst��rstellen-Anderson-Modell reproduziert werden. Die BMN in zweiter Ordnung ist nicht in der Lage, die Oszillationen, die durch die Banddiskretisierung im Kontext der NRG entstehen, vollst��ndig zu d��mpfen, kann jedoch durch die wohlbekannte z-Mittelung konstruktiv erg��nzt werden. Es stellt sich heraus, dass der BRF ineffizient ist f��r wechselwirkende Systeme, in denen die lokale Wechselwirkung die Bandbreite ��bersteigt. Hierzu diskutieren wir mehrere alternative Optionen. Die Motivation dieser Arbeit ist rein methodologischer Natur, weshalb wir uns auf die einfachsten Quantenst��rstellenmodelle beschr��nken. Der OWF ist allerdings ebenso vielf��ltig einsetzbar wie die NRG selbst, und damit anwendbar auf z.B. Multi-St��rstellenmodelle oder lokalen Gleichgewichts- und Nicht-Gleichgewichts-Transport., We present an approach for quantum impurity systems that extends the numerical renormalization group (NRG) to an open quantum system formulation. The continuous conduction band is divided into an arbitrary Wilson chain and a set of reservoirs without affecting the local bath hybridization function. One reservoir is coupled to each chain site and is treated by the Bloch-Redfield formalism (BRF), which includes the Born-Markov approximation (BMA). This open chain formalism (OCF) yields true thermalization in local real-time non-equilibrium dynamics, as well as finite lifetime in local equilibrium spectral functions. It reproduces the t ��� ��� steady-state predicted by the NRG and the correct relaxation rates in the resonant level model. By enlarging the Wilson chain, the accuracy of the BMA, especially with respect to short-time dynamics, is increased. The formation of Hubbard-peaks and the Kondo-resonance are reproduced for the single-impurity Anderson model. The BMA in second order results in the persistence of finite-size oscillations to some degree, which can be damped by the well-established procedure of z-averaging. We find the BRF to be inadequate for interacting models, if the local Coulomb repulsion exceeds the conduction bandwidth, and discuss several options to improve the OCF for this parameter regime. Since the motivation for this thesis is of pure methodological nature, we restrict to the most simple quantum impurity models to benchmark our algorithm. However, the OCF is as versatilely applicable to more complex models as the pure NRG. Consequently, our approach can be adapted to e.g. multi-impurity models, as well as simulate local transport properties in and out of equilibrium.

We study the interplay between Mott physics, driven by Coulomb repulsion U, and Hund physics, driven by Hund's coupling J, for a minimal model for Hund metals, the orbital-symmetric three-band Hubbard-Hund model (3HHM) for a lattice filling of 1/3. Hund-correlated metals are characterized by spin-orbital separation (SOS), a Hund's-rule-induced two-stage Kondo-type screening process, in which spin screening occurs at much lower energy scales than orbital screening. By contrast, in Mott-correlated metals, lying close to the phase boundary of a metal-insulator transition, the SOS window becomes negligibly small and the Hubbard bands are well separated. Using dynamical mean-field theory and the numerical renormalization group as real-frequency impurity solver, we identify numerous fingerprints distinguishing Hundness from Mottness in the temperature dependence of various physical quantities. These include ARPES-type spectra, the local self-energy, static local orbital and spin susceptibilities, resistivity, thermopower, and lattice and impurity entropies. Our detailed description of the behavior of these quantities within the context of a simple model Hamiltonian will be helpful for distinguishing Hundness from Mottness in experimental and theoretical studies of real materials.