Research Projects

A comprehensive understanding of quantum many-body systems (QMBS) requires insight into both the nature of individual phases and the mechanisms driving phase transitions between them. Although the specific origins of phase transitions can vary widely across systems, they often exhibit universal characteristics governed by the framework of critical phenomena. These shared features are captured by universal scaling laws and renormalization group principles, which provide deep insights into the behavior of diverse physical systems near criticality. Importantly, quantum many-body systems not only exhibit rich phase diagrams and exotic states in static or equilibrium conditions, but can also host novel non-equilibrium phases and emergent phenomena when driven dynamically—for example, through time-periodic driving, quantum quenches, or coupling to external environments. These driven systems often fall outside the scope of traditional equilibrium statistical mechanics and may give rise to entirely new universality classes and functionalities. It is of paramount importance to develop a unified understanding of critical phenomena and novel phase structures in both equilibrium and non-equilibrium settings. Such exploration not only addresses foundational questions in physics but may also enable new functionalities in quantum materials and devices, with potential relevance for future quantum technologies. The goals of my research are to explore novel phases, and physical properties in a variety of quantum many-body systems, both in and out of equilibrium. A key focus is on understanding the nature of quantum phase transitions, including the role of interactions, symmetry breaking, topology, and dynamical driving protocols, using both analytical and numerical tools. For Focus 1 and Focus 2, the project will employ field-theoretical techniques commonly used in the study of quantum many-body systems. These include perturbation theory and renormalization group (RG) methods to analyze phase transitions and emergent phenomena in correlated electronic systems. Computational work will be carried out using programming languages such as C, Mathematica, and Python to perform symbolic and numerical calculations. In Focus 3, the investigation of non-equilibrium quantum many-body systems will utilize non-equilibrium Green’s function techniques and Floquet theory to analyze periodically and aperiodically driven systems. Numerical approaches such as exact diagonalization will be employed to study time evolution, thermalization dynamics, and the emergence of steady states in small to intermediate-sized systems.