Typical Eigenstate Entanglement of Spinless Fermions

CAM Conference 2017, Washington DC

In a seminal paper, Don Page computed the entanglement of typical states representing all states in the Hilbert space and found that these are maximally entangled in the thermodynamic limit. In our work, we study the entanglement entropy of eigenstates of spinless fermion Hamiltonians and find that the entanglement of typical eigenstates is vastly different from typical states in the Hilbert space. We prove this by deriving analytical bounds of the entanglement entropy averaged over all eigenstates as a function of the subsystem size.