Multi-entropy in Chaotic Eigenstates

Entanglement measures provide essential tools in the characterization of the non-local correlations of quantum phases of matter. In recent years, there has been considerable progress in uncovering the structure of many-body tripartite entanglement using quantum information theoretical quantities like reflected entropy and multi-entropy. In this work, we investigated multi-entropy in chaotic eigenstates as a potential finer probe for the correlations and structure in such states. Specifically, using a tripartite generalization of the ergodic bipartition conjecture, we derived an analytical expression for multi-entropy and related tripartite entanglement quantities in energy eigenstates of chaotic many-body Hamiltonians. We numerically tested this expression in the mixed field Ising model using exact diagonalization, and found that the analytical prediction matches the numerical results well across a range of Hamiltonian parameters and eigenstate energies. We also studied the structure of the ρ_AA^*, the reduced density matrix associated to the canonical purification state which is involved in the computation of the reflected entropy, in chaotic many-body systems.