Research

Aspects and Applications of Chern-Simons Theories

We studied the geometrical setting of Chern-Simons theories and their quantization on various interesting manifolds in three dimensions. We calculated the Feynman diagrams of Chern-Simons theories coupled to bosons in the fundamental representation and discussed the applications of Chern-Simons matter theories in the quantum mechanics of non-Abelian anyons and as effective field theories of quantum Hall effects.

[Thesis]

Neural Belief Propagation Decoding of Sparse Quantum Codes

We extended the Neural Belief Propagation algorithm to decode quantum error correcting codes under experimentally relevant noise models. We implemented the neural networks in PyTorch and simulated stabilizer circuits using Stim.

[Report]

Prethermalization in Aperiodically Driven Classical Spin Systems

We discover a novel thermalization time scaling law for classical spin systems subject to random multipolar drives. We also establish the presence of classical discrete time-crystalline phases of matter in the prethermal plateau. The thermalization process in the classical systems we study is parametrically slower than their quantum counterparts.

[Phys. Rev. E 110, 064150] [arXiv]

Geometric Phases in Optics

We explored the possibility of demonstrating the geometric phase of light in angular momentum space using Laguerre-Gaussian beams. We also built an experimental setup to demonstrate the Panchratnam-Berry phase.

Course Projects

RIXS Spectrum of the Kitaev Chain

We computed the resonant inelastic X-ray scattering (RIXS) spectrum of the Kitaev chain in the spin conserving channel using tensor network methods.

[Report]

Scrambling Dynamics in Classical and Quantum Systems

We used time evolving block decimation and time-dependent variational principle algorithms to compute the out-of-time ordered correlators for interacting quantum systems. We also compute the decorrelator for classical systems.

[Report] [Presentation]

Gamma Matrix Model for Algebraic Spin Liquid

We studied an exactly solvable model for algebraic spin liquid using Kitaev's fermionization technique.

[Report] [Presentation]

Pruned-Enriched Rosenbluth Method for Simulating Polymers on Lattices

We simulate polymers as self-avoiding random walks on two and three-dimensional lattices and compute the average end-to-end distance using Monte Carlo methods.

[Report]

Topological Quantum Error Correction

We studied the stabilizer formalism and braiding of anyons in the toric code for quantum error correction. We also implement the repetition code in Qiskit.

[Presentation]

Divergences in Perturbation Theory

We studied Dyson's argument for divergence of the perturbation series in quantum electrodynamics and learned techniques for resummation of divergent series.

Estimation of Electronic Band Gap Energy From Material Properties Using Machine Learning

We implemented a novel ensemble learning algorithm in scikit-learn to estimate the electric band gap. We trained the machine learning model on the AFLOW dataset.

[IEEE Xplore]

Miscellaneous

The video of my talk titled "Spontaneously Broken Time Translation Symmetry: Time Crystals" in Vikiran, the Physics club of NISER.