Research Projects

The focus of this project is on pushing the boundaries of classical computations using the power of parallel computing computation on GPUs for addressing ambitious questions in strongly correlated condensed matter physics, broadly under two major umbrellas: a. Distinguishing between phases in strongly correlated topological matter, using entanglement and other Quantum information markers as probes: The classical phase classification of matter, rooted in the Landau paradigm and spontaneous symmetry breaking, explains phenomena like superconductivity and ferromagnetism with a critical temperature separating ordered and disordered phases. However, the discovery of the integer Hall effect introduced topological order, leading to a new classification of phases without symmetry breaking. This evolution has spurred intense research into topological phases, blending physics and mathematics. While a robust theory exists for weakly interacting electrons, understanding strongly correlated topological phases remains limited, especially in two dimensions, due to computational and analytical challenges, which this research aims to address. b. Strong correlation induced ergodicity in various quantum phases in Flat-band systems. Flat bands, characterised by dispersionless states, have garnered interest due to their observation in materials like Kagome metals and twisted bilayer graphene, and their connection to gravitational physics via holography. These bands result from the destructive interference of electron wavefunctions, leading to ultra-localized states with symmetries linked to Carroll manifolds. Using these localised states, one can create strong correlations and exotic phases. However, understanding their stability under perturbations remains a challenge. Studying these systems requires advanced computational methods like tensor networks and GPU-based parallel computing, which are crucial for understanding their complex behaviours and potential transitions to transport or thermalised phases. Attacking the physics problems addressed above is indeed a challenge in computational science i.e. solving large-scale eigenvalue problems as well as matrix reshaping and contractions efficiently on heterogeneous hardware. From this perspective, this problem is tightly coupled with key research areas such as parallel algorithm design, memory hierarchy optimisation, and GPU computing. The work explores novel task scheduling and memory management strategies to mitigate GPU memory bottlenecks, with an emphasis on developing scalable and portable software solutions. Such innovations directly contribute to the fields of HPC and scientific computing by enabling efficient handling of data-intensive computations that exceed the capacity of conventional GPU memory. The Physics questions are of fundamental nature with ambitions to connect with futuristic quantum materials discovery. These problems connect expertise and ideas from a diverse sector. However, the outputs in the computational side, aided by the physics questions, are of more practical usage with a foreseeable product-ready stage near the end of the project tenure. The figures of merit for the computational works are established on a cloud-based facility. With efficient algorithms, we found eigenvalues (with precision of 1 in a million parts) of a Hamiltonian describing a strongly correlated fermionic system whose Hilbert space is of dimension around 60 thousand, within 5 minutes. For accurate prediction, which can be reliably extrapolated to larger systems, we need to scale up the computational power. The numerical tasks/ experiments will be carried out on medium-scale GPU equipment, to be procured with the present project’s financial assistance. With benchmarked results, algorithmic developments will be done, and for further scaling up, we would request access to national facilities deployed under the National Supercomputer Mission at various academic institutes.