Executive Summary : | Quantum entanglement allows distilling the true nature of quantum states of multiple degrees of freedom. As a result, entanglement has emerged as an important measure in condensed matter physics to probe novel many-body states. Recent advancements in the field have revealed intriguing connections between entanglement, quantum dynamics, and thermalization. Entangled quantum states could also become one of the main resources for future quantum computation, having significance for quantum information, cryptography, and error correction. However, the full potential of entanglement for quantum computation and characterizing physical systems has not been understood yet. This is because quantifying and calculating entanglement and its dynamics in the presence of an environment or other degrees of freedom is challenging. Entanglement can be quantified in terms of von Neumann, Rényi entanglement entropies and entanglement negativity. However, computing these entanglement measures are much more challenging than thermodynamic entropy. The main objective of the proposed project would be to develop new theoretical methods to compute measures of entanglement for interacting systems of fermions and spins, in and out-of-equilibrium. The basis of these methods would be a new formulation of entanglement measures in terms of many-body path integrals, developed very recently by the PI and his collaborators. The path integral allows a very transparent generalization of various standard techniques and methods of quantum many-body physics, e.g., diagrammatic perturbation theory, mean-field approximations etc., to compute entanglement. Both closed and open systems, i.e., systems in the absence and presence of an environment, respectively, will be investigated. PIs will characterize phases and quantum dynamics in terms of various entanglement measures for several closed and open interacting systems with correlated ground states, as well as systems with non-trivial symmetry-protected topology and topological order. Thus, in the context of studies of entanglement in interacting systems, the major gap area that the proposal aims to address is the lack of a single general transparent quantum many-body method, at the level of standard quantum field theory formalism, that can be applied with various level of approximations with known range of validity. The pure and mixed-state entanglement measures like Rényi entropy and negativity will be studied as a function of the linear size of a subsystem and the size of the entire system. The project will investigate the effects of strong correlation, disorder, coupling to bath, external drive, and measurements on the universal and non-universal parts of entanglement measures. The project will also study entanglement dynamics of high-energy pure states, obtained by evolving unentangled product states under unitary time evolution, e.g., disordered Hubbard Hamiltonian across many-body localization transition. |