Research Projects

The study of entanglement between various subsystems of a given state in quantum mechanics has a long history. It is also deeply connected with the idea of entropy, a bedrock for statistical mechanics and thermodynamics. It provides the measure of entanglement between various subsystems and goes by the name of entanglement entropy (EE). One can ascribe an operator equivalent to EE, known as modular Hamiltonian (H), whose expectation value computes this entropy for us. However, for quantum field theories (QFT), the idea of entanglement for a multi-partitioned system (e.g. where the original Hilbert space has been factorized) is more subtle. The EE in these cases turns out to be ultraviolet divergent, already hinting at the fact that such bi-partition requires more care. It also means that it is not just the property of the states, but also of the algebra of the observables. The project under consideration will deal with such fundamental issues in field theory. In QFT suppose we want to consider entanglement of a subregion with its complement. It turns out that another probe of the above non-factorizability lies in the study of H for an arbitrary excited state. Starting with a ground state and exciting this state by a unitary operator (in space or null-like directions, for specificity), the resulting change in H is no longer the expected unitary transformation, but rather involves an additional contribution arising out of the endpoints (the points where the subregions meet). In our previous works, we have taken a first step towards the study of these endpoint contributions and via this project, we want to take our ideas and results further. So far, our results are perturbative (in a parameter controlling the unitary excitation) and it begs for a non-perturbative generalization. Although much of the results are applicable for QFT, for computational purposes, conformal field theories (CFT) give us a better handle. We would thus like to generalize our results by studying such a problem from different perspectives (e.g. using path integral). Moreover, in situations where the CFT has a holographic dual (as in Anti de Sitter (AdS)/ CFT correspondence of string theory), then these endpoint contributions have significant implications for the locality and operator algebra on the gravitational side. In that case, our results translate to the entanglement structure of quantum gravity itself. The study of entanglement in field theory provides a novel perspective towards the intricacies of dealing with continuum theories and associated von- Neumann algebras which has been a focus of current research in theoretical physics community. This research direction is new and unfolding, and will be a perfect playground for students and postdocs.

Entanglement in field theory, Modular Hamiltonian, AdS/CFT duality, black holes, Information and gravity