Research Projects

Gauge theories are fundamental to high-energy particle physics and vital for understanding various low-energy condensed matter phenomena, such as topological order and quantum spin liquids. However, accurately simulating gauge theories poses significant challenges due to limitations in traditional computational methods like quantum Monte Carlo (QMC), which faces the sign problem for finite fermionic densities or during real-time dynamics. This project aims to overcome these computational obstacles and advance the study of lattice gauge theories (LGTs) by utilizing emerging tools from quantum science and technology, particularly tensor network (TN) algorithms and synthetic quantum simulator platforms. Recent experimental progresses in synthetic quantum platforms, including ultracold atoms, superconducting circuits, Rydberg arrays, and ion traps, have brought digital and analog quantum simulations of LGTs closer to reality, and plethora of experiments and experimental proposals towards the scalable quantum simulation of LGTs in near future have emerged in literature. In the computational domain, TN algorithms have transformed the landscape of simulating strongly correlated many-body systems by overcoming limitations of QMC. Using matrix-product state (MPS) ansatzes, various Abelian and non-Abelian LGTs have been studied in 1+1D, with ongoing efforts to analyze 2+1D and even 3+1D LGTs using tree-tensor networks (TTN) and projected entangled pair states (PEPS). Building on the momentum, the project will focus on three broad goals. First, it will investigate synthetic quantum systems, particularly multi-species and multi-component Rydberg atom arrays, where gauge invariance can emerge in low-energy limits. These systems enable scalable simulations of LGTs without the need of implementing complex multi-body interactions. Second, the project will employ advanced TN methods, such as MPS, TTN, and PEPS, to study equilibrium and dynamical behaviors of non-Abelian LGTs in 1+1D and 2+1D. This exploration is crucial for understanding complex phenomena like confinement-deconfinement transitions, topological properties, or real-time particle production, which traditional methods struggle to capture. Finally, the project aims to develop a gauge-invariant TN framework for Abelian gauge theories, enhancing the accuracy and efficiency of future numerical simulations. This research aligns closely with India's National Quantum Mission (NQM) and complements major international initiatives for simulating LGTs within quantum technologies. It is poised to make significant contributions to TN methodologies and quantum simulators for gauge-invariant systems, potentially addressing unresolved questions in particle physics, condensed matter, and quantum information. Expected outcomes include new theoretical insights, published research findings, and the development of open-source computational tools to enhance community access and foster collaboration.