Entanglement at the interplay between single- and many-bodyness

Abstract

Abstract The tensor network representation of the ground state of a Bethe chain is analytically obtained and studied in relation to its entanglement distribution. Block entanglement displays a maximum at the interplay between single- and many-bodyness. In systems of two fermions, tensor networks describing states with substantial many-body entropy cannot be written as a sequence of next-neighbor unitaries applied on an uncorrelated state, but need four-next-neighbor unitaries in addition. This differs from the idea that ground states can be obtained as a sequence of next-neighbor operations applied on an initial tensor network lacking many-body correlations. The work uncovers the transcendence of the notion of many-bodyness in the implementation of protocols based on matrix product states.