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Modeling polarons in transition-metal oxides Lau, Bayo


This work is a series of reports on progress in the description of electron-electron and electron-lattice interactions in transition-metal oxides, with an emphasis to the class of high-Tc superconducting cuprates. Combinations of numerical and analytical approaches were devised and developed to study large-scale models, which distinguish cation and anion sites of the realistic lattice structure. The many results range from incremental deviation to significant difference compared to those of the widely-accepted simple models without such distinction. A previously proposed numerical scheme and a perturbation approach were adapted to study the one-dimensional breathing-mode model, which describes a charge carrier interacting with vibrating anions. The effort yielded the first accurate benchmark result for all parameters values of the model. Based on a physical insight about the spin-1/2 Heisenberg antiferromagnet on a two-dimensional square lattice, an octapartite approach was devised to model the low-energy states. The efficiency of the resulting numerical approach was showcased with the explicit solution to a record-breaking 64-spin torus. A spin-polaron model was derived to model holes injected into cuprate's quasi two-dimensional copper-oxygen layer. Total-spin-resolved exact diagonalization was performed for a single fermionic hole in a record-breaking cluster with 32 copper and 64 oxygen sites. The solutions revealed important physics missed by previous studies. The octapartite approach was then developed to solve the spin-polaron model with two extra holes in the same cluster. The accuracy and efficiency of the method were established. Enhanced singlet correlation between two holes was observed. The preliminary results justify the need for an in-depth study.

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