Research Projects

The field of quantum condensed matter has made significant strides in understanding emergent phenomena in experimentally and technologically relevant systems where strong correlations, topology, and disorder play significant roles. However, crucial questions remain, especially regarding gapless or metallic quantum matter in low-dimensional systems, arising at quantum critical points and where quasi-particles strongly interact. This project targets two such areas: Quantum Hall (QH) transitions and anomalous quantum metals, with each providing a unique avenue for exploring major themes in quantum condensed matter. Quantum Hall Transitions: QH phases are the paradigmatic topological phases of matter that launched the field into a new direction in the 1980s. While the phases are well understood, how the transition between two different QH phases takes place is an unsolved but one of the most important problems in our field. A fundamental question is the superuniversality conjecture that connects all these transitions. Founded on experimental observations, it suggests that both integer (IQH) and fractional QH (FQH) transitions exhibit the same critical exponents despite their distinct origins. The former can arise from non-interacting fermions while the latter are fundamentally strongly-interacting. Our goal is to test this conjecture by constructing a unified framework for IQH and FQH transitions using the composite-fermion model, incorporating topology, interactions and disorder. Using both quantum field theory and model wavefunctions, we aim to study whether critical properties are altered when IQH transition is transformed into an FQH one. Analytical perturbation theory, Hartree-Fock and Monte-Carlo methods will be employed to evaluate the relevance of perturbations around the IQH critical point, potentially solving the superuniversality puzzle. Anomalous Quantum Metals: Experimental observations of metallic phases near superconductors in 2+1D pose a theoretical challenge since the conventional scaling theory of localization predicts their absence in 2+1D. We propose that it arises due to vortices experiencing long-range interactions alongside disorder. Our approach is novel in the sense that we attempt to construct a mean-field theory using fermionic vortices. We plan to numerically simulate the physics of vortices using Hartree-Fock method and in parallel their semiclassical dynamics. By examining the transport properties as a function of vortex density, we aim to uncover new insights into the emergence of metallic behavior near 2D superconductors. Achieving these objectives will provide much needed novel perspectives on fundamentally significant problems in quantum condensed matter physics. Theoretical understanding of these phenomena has lagged behind experiments; our approach seeks to bridge this gap. Successful outcomes from this research program will lead to breakthroughs that could drive the field into new and impactful directions.