Research Projects

Quantum complexity has recently emerged as the universal tool to characterize quantum systems with very large numbers of degrees of freedom which are strongly interacting and strongly correlated. Independent lines of research across fields as diverse as computer science, condensed matter, statistical physics, quantum gravity have converged and led to the identification of quantum complexity as the essential property of strongly interacting, strongly correlated many-body systems which capture their collective quantum dynamics. The Hilbert space of such large complex systems scale exponentially with system size, and traditional tools of many-body physics or quantum field theory (QFT) - be it analytical or numerical, are of limited utility and have only led to modest progress in demystifying their complex behavior. Our proposal is a response to the need of the hour - to explore quantum complexity via complementary approaches in different contexts, from many-body physics to field theory and gravity, analytically and numerically. The proposed work will build on our findings in the recent past, where complexity led to new conceptual insights and computational simplifications in quantum phase transitions, quantum chaos, scrambling and thermalization, and demystified black hole physics and strongly coupled field theories. The first problem we propose to attack with our complexity approach is that of quantum chaos, which underlies the dynamics of the majority of large quantum systems. Krylov complexity has great promise since it captures the notion of operator growth bearing the signature of quantum chaos. This would be our principal tool to study decoherence, thermalization and strong coupling regimes of many-body systems. We also aim to apply Krylov complexity to capture chaotic phenomena associated with the S-matrices in field theories. The second problem we would like to tackle concerns the Circuit Complexity of states in a field theoretic setting. This concept is not well defined in the continuum limit. To fully harness the potential of circuit complexity, we intend to work beyond heuristic frameworks in weakly coupled systems- in the process, one has to resort to advanced mathematical results and potentially introduce new concepts from group theory, topology and geometry. This is fueled by our preliminary findings in recent publications, where we utilized such mathematical tools for circuit complexity while exploring recently developed holographic dualities. Next, we would further like to use circuit complexity to study renormalization group (RG) flows in a variety of systems in condensed matter and high energy physics. In particular, the tensor network representation of ground state wavefunctions of lower dimensional systems provides access to many physical quantities which were beyond the scope of traditional approaches. Complexity is touted to play a major role because complexity effectively quantifies the size of the network.