Entanglement patterns in local quantum chaotic Hamiltonians with symmetries

Quantum chaos in many-body quantum systems is typically understood in terms of the random matrix theory (RMT) behavior of eigensystem properties, particularly eigenstates and their energy level statistics. Although RMT has been remarkably successful in describing the `coarse' features of quantum states in chaotic regimes, such as the volume-law behavior of the entanglement entropy (EE), it fails to capture their `finer' structures, such as O(1) corrections to the EE or its statistical fluctuations, arising from spatial locality or additional symmetries. In this talk, I show how to describe the statistical behavior of eigenstates in quantum chaotic Hamiltonians by constraining RMT ensembles to account for the effects of spatial locality and, possibly, additional symmetries. I demonstrate the approach in a variety of widely-used physical Hamiltonians with increasingly more complex internal structures, such as particle number conservation or non-abelian symmetries.