Nuñez Fernández, Yuriel (2018) Desarrollo y aplicación de métodos computacionales de avanzada para el calculo de propiedades electrónicas de materiales correlacionados. / Development and application of advanced computational methods for the calculation of electronic properties of correlated materials. Tesis Doctoral en Física, Universidad Nacional de Cuyo, Instituto Balseiro.
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Resumen en español
Estudiamos varios modelos paradigmáticos de materiales correlacionados usando la teoría de Campo Medio Dinámico (DMFT) bajo un tratamiento unicado. El problema auxiliar de impureza generado en las iteraciones DMFT se resuelve usando Renormalización basada en la Matriz Densidad (DMRG), con vector corrección, de forma que todas las escalas de energía se tratan con igual precisión y la densidad de estados (DOS) se obtiene en el eje real. Calculamos modelos tipo Hubbard, Hubbard-Hund y Kanamori-Hubbard, teniendo en cuenta la interacción de Coulomb intra (inter) orbital U (U_12) y el acoplamiento de Hund J, en la red de Bethe y red cuadrada, de una o dos bandas (con o sin hibridización interorbital), sistemas semillenos y dopados. Así logramos caracterizar fenómenos bien conocidos como la transición metal-aislante de Mott a temperatura cero, y otros interesantes como la transición de Hund y la transición selectiva en orbital. Con la idea de estudiar correlaciones espaciales, para un modelo tipo Hubbard de una banda en la red cuadrada, inspirado en los cupratos, implementamos el cluster-DMFT de 2 y 4 sitios, en su variante celular. Logramos reproducir preliminarmente resultados obtenidos con otras técnicas numéricas, pudiendo obtener la DOS directamente en el eje real con baños hasta 4 veces más grandes que los considerados hasta ahora, con lo cual se reduce el efecto de tamaño finito. Estudiamos el modelo de Hubbard de dos bandas en la red cuadrada en presencia de hibridización interorbital entre primeros vecinos y desdoblamiento por campocristalino. Encontramos que dicha hibridización siempre lleva a una DOS local finita en la energía de Fermi en los dos orbitales cuando al menos una de las bandas es metálica. Cuando los parámetros del modelo son tales que el potencial químico está en la banda de Hubbard del orbital 1 y entre las bandas de Hubbard del orbital 2, en este último aparece un pico de cuasipartícula en el nivel de Fermi cuyo peso decae exponencialmente con la interacción U. El comportamiento es similar a la física de Kondo donde la banda 1 hace el papel de baño no interactuante. En un modelo de dos bandas tipo Hubbard-Hund invariante rotacional, caracterizamos el espacio de parámetros U, J. Observamos la transición metal-aislante al aumentar U (transición de Mott) y también al aumentar J (transición de Hund). Calculamos el peso de cuasipartícula y obtuvimos que, para J ≠ 0, la transición de Mott es de primer orden como función de U y es de segundo orden para J = 0. Estos resultados están de acuerdo con el comportamiento obtenido por colaboradores usando bosones esclavos y también Monte Carlo cuántico. En modelos tipo Hubbard-Kanamori de dos bandas iguales, nuestros resultados sugieren que la transición de Mott es de primer orden cuando U_12 ≤ U y es continua cuando U_12 = U o cuando U_ 12 < U/2. Para bandas diferentes, obtuvimos la transición de Mott selectiva en orbital. Observamos que ésta es estable frente a la hibridización interorbital (t´) si U_12 ≤ U/2, coincidiendo con otros autores, mientras que desaparece con t´ si U_12 ≤ U. Nuestros resultados poseen la ventaja de mostrar la DOS en el eje real de frecuencias. Estudiando estos modelos de dos bandas, encontramos unas excitaciones novedosas, que aparecen como picos en la DOS, en energías del orden de ∆ = U - U_12 para la fase metálica, hasta ahora no reportados en la literatura. Caracterizamos las cuasipartículas asociadas a estas excitaciones, concluyendo que son pares hueco-doblón interorbital. Una DOS finita en la energía de Fermi de una banda está correlacionada con el surgimiento de estados de cuasipartícula bien definidos a energías ∆ en la otra banda. Una importante consecuencia de este mecanismo es que en el caso simétrico U_12 = U el pico de esta cuasipartícula se sitúa en la energía de Fermi, sin importar si una banda es mucho más angosta que la otra. Esto significa que ambas bandas son metálicas mientras una lo sea: no hay transición selectiva. Nuestros cálculos confirman esta predicción y además muestran que, para una relación de 1/50 de los anchos de banda, el pico en la energía de Fermi en la banda ancha aparece por el mecanismo de Kondo mientras que en la banda angosta aparece debido a las mencionadas cuasipartículas. Este resultado da por terminada una controversia de más de una década entre diferentes autores donde algunos sostenían que podía haber una transición selectiva cuando el cociente de los anchos de banda fuese menor que 1/5. Gran parte de esta tesis estuvo abocada al desarrollo de métodos computacionales de avanzada para el cálculo de las propiedades mencionadas arriba. Desarrollamos tres softwares de libre acceso para la diagonalización exacta, el DMRG y el DMFT, respectivamente, con la suficiente eficiencia, generalidad y abstracción para poder tratar todos estos problemas a la vez y que puedan ser extendidos fácilmente a nuevos modelos o parámetros. Un aporte relevante fue la implementación del DMRG para la impureza efectiva que forma parte esencial del DMFT. Para esto, para la impureza efectiva representamos la hibridización en forma de estrella (ver Figura 3.3) -y separada en espín- y no en forma de cadena como se hacía tradicionalmente, mejorando considerablemente el costo de los cálculos. El mismo programa DMRG permite hacer cálculos de hamiltonianos generales tipo química cuántica, tanto del estado fundamental como de la respuesta dinámica. La técnica desarrollada en esta tesis es una de las más adecuadas y confiable para el cálculo de estructura electrónica a temperatura cero de sistemas correlacionados.
Resumen en inglés
We study several paradigmatic models of correlated materials using the Dynamical Mean Field Theory (DMFT) under an unied treatment. The auxiliary impurityproblem generated in the DMFT iterations is solved with the Density Matrix Renormalization Group (DMRG), using the correction vector, so that all energy scales are treated on equal footing and the density of states (DOS) is obtained in the real axis at zero temperature. We calculate Hubbard, Hubbard-Hund and Kanamori-Hubbard type models, taking into account the intra (inter) orbital Coulomb's interaction U (U_12) and the Hund exchange coupling J, in the Bethe lattice and in the square lattice. We considered one and two bands with and without interorbital hybridization, and half-lled and doped systems. We characterized well-known phenomena such as the metal-insulator Mott transition, and other interesting physical phenomena such as the Hund transition and the orbital-selective transition. To study spatial correlations for the one-band Hubbard model in the square lattice, we implemented the celular-DMFT with 2 and 4 sites. We reproduce previous results obtained with other numerical techniques, being able to obtain the DOS directly on the real axis with baths up to 4 times larger than those considered up to now, which reduces the nite-size effects. We study the two-band Hubbard model in the square lattice including nearestneighbors interorbital hybridization and crystal-eld splitting. We find that such hybridization always leads to a nite DOS at the Fermi energy for both orbitals when at least one of the bands is metallic. When the parameters of the model are such that the chemical potential is at the lower Hubbard band of the orbital 1 and between the Hubbard bands of the orbital 2, a quasi-particle peak appears for the orbital 2 at the Fermi level, whose weight decays exponentially with the interaction U. This behavior is similar to the Kondo physics where band 1 plays the role of the non-interacting bath. For a two-band Hubbard-Hund model with rotational-invariant interaction, we characterize the parameter space U, J. We observe the metalinsulator transition when increasing U (Mott transition) and also when increasing J (Hund transition). We calculate the quasiparticle weight and we obtain that, for J ≠ 0, the Mott transition is first-order as a function of U and it is second-order for J = 0. These results are inagreement with the behavior obtained by collaborators using slave-bosons and Quantum Monte Carlo techniques. For Hubbard-Kanamori models of two equal bands, our results suggest that the Mott transition is first-order when U_12 ≤ U and it is continuous when U_12 = U or when U_12 < U/2. For different bandwidths, we obtain the orbital-selective Mott transition. We note that it is stable against interorbital hybridization (t´) if J = U/4; U_12 = U/2, in agreement with other authors, while disappearing with t´´ if U_12 ≤ U. Studying these two-band models, we nd novel excitations, which appear as peaks in the DOS, for energies of order = U U12 for the metallic phase. We characterize the quasiparticles associated with these excitations, concluding that they are interorbital holon-doublon pairs. We find that a nite density of states at the Fermi energy in one band is correlated with the emergence of well defined quasiparticle states at excited energies ∆ in the other band. An important consequence of this mechanism is that in the symmetric case U_12 = U the peak of this quasi-particle lies at the Fermi energy, regardless of whether one band is much narrower than the other. This means that both bands are metallic as long as one is metallic and there is no selective Mott transition. Our calculations show that, even for very small bandwidth ratios, the peak at the Fermi energy in the wide band is formed by the Kondo mechanism while it appears in the narrow band due to the mentioned quasiparticles. This result ends a long-standing controversy between different authors where some argued that there could be a selective transition when the bandwidth ratio was less than 1/5. Much of this thesis was devoted to the development of advanced computational methods for calculating the above mentioned properties. We develop three open-source softwares for the exact diagonalization, the DMRG and the DMFT, respectively, in an efficient, general and abstract form such that they are able to treat all these problems at the same time and they can easily be extended to new models or parameters. A relevant contribution was the implementation of the DMRG for the eective impurity that forms an essential part of the DMFT. For this, we use the star-geometry representation of the hybridization, also separated by spin, instead of the chain-geometry representation as was traditionally done, considerably improving the cost of calculations. The same DMRG program allows calculations using a general quantum-chemistry Hamiltonian for both the ground state and the dynamic response. The technique developed in this thesis is one of the most adequate and reliable numerical methods for the calculation of electronic structure of correlated systems at zero temperature.
| Tipo de objeto: | Tesis (Tesis Doctoral en Física) |
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| Palabras Clave: | Electronic structure; Estructura electrónica; [Correlated materials; Materiales correlacionados; Computational methods; Métodos computacionales ] |
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| Materias: | Física > Materia condensada |
| Divisiones: | Gcia. de área de Investigación y aplicaciones no nucleares > Gcia. de Física > Materia condensada > Teoría de sólidos |
| Código ID: | 784 |
| Depositado Por: | Tamara Cárcamo |
| Depositado En: | 24 Feb 2021 11:41 |
| Última Modificación: | 24 Feb 2021 11:41 |
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