Entanglement dynamics of many body quantum states with evolving system conditions

The entanglement analysis of a pure state of a many body quantum system requires a prior information about its density matrix/ state matrix, obtained in principle by solving the Hamiltonian matrix. The missing information due to complexity of the many body interactions however renders it necessary to consider an ensemble of Hamiltonians and thereby an ensemble for each eigenstate. This in turn leaves a statistical description of the entanglement measures as the only option. For an ensemble to appropriately represent a many body Hamiltonian, the ensemble parameters must be determined from the system parameters. A variation of the latter is therefore expected to manifest in variation of the the ensemble for each eigenstate and thereby their entanglement aspects. We theoretically analyze the effect of varying system conditions on the eigenstates of a wide range of Hamiltonians and derive a common mathematical formulation for the bipartite entanglement statistics. As the system information in the formulation enters through a single functional of the ensemble parameters, this implies the analogy of statistics for different eigenstate ensembles (non-Haar type) if they share the same complexity parameter and thereby reveals a deep web of connection underlying among quantum states of different Hamiltonians (with same global symmetry class). Besides revealing universality among non-haar states, the information is also relevant for quantum state engineering e.g. how to achieve a near Haar random state starting from a random non-ergodic state.
Work done in collaboration with my PhD student Devanshu Sekhar.