Theoretical Investigations of Spectral Properties of Ordered and Disordered Strongly Correlated Electronic and Spin Systems

Abstract

The Thesis is thematically divided into four broad parts: The first part (Chapters 1-2) introduces ordered and disordered correlated many-body quantum systems and outlines relevant analytical and numerical methods essential for understanding their eigenvalues and eigenstates. The second part (Chapters 3-5) focuses on studying the Spectral Correlation Statistics in one- and two-dimensional disordered quantum systems, employing various statistical techniques, including RMT, to explore eigenvalue correlations in single-body and many-body quantum chaotic systems. While single-body quantum chaotic systems, like the Quantum Kicked Rotor and chaotic quantum Billiards, have intuitive classical counterparts, the complexity increases when studying the two many-body interacting quantum chaotic spin systems (Model-I and Model-II) with various exchange interactions and intrinsic (random couplings, etc.) or extrinsic (coupled to stochastic fields, etc.) disorder. The third part (Chapter 6) investigates the behavior of the eigenstates in Model-I and Model-II across integrable and chaotic regimes, classifying them as ergodic, localized, fractal, or multifractal, and analyzing their singularity spectrum. In the fourth part (Chapter 7), the focus shifts to complex ordered correlated electronic systems, like high-Tc Cuprates, involving the development of computational codes for High-energy Optical Conductivity and Anomalous Spectral Weight Transfer (this was undertaken as a part of the DST-SERB Project: ECR/2016/002054). We also qualitatively reproduce the strong polarization and doping dependence of the high-energy optical spectra and its well-known dependence on the magnetic background. The Thesis concludes with an Epilogue (Chapter newline newline8) presenting a summary of the Thesis.