Construction and Universal Application of Entanglement-Erasing Partner States

We investigate the subadditivity of the bipartite entanglement entropy (EE) of many-particle states, represented by Slater determinants, with respect to single particle excitations. In this setting, subadditivity can be phrased as erasure of EE, i.e., as a relative decrease in EE when adding excitations to the quantum state. We identify sets of single particle states that yield zero EE if jointly excited. Such states we dub entanglement erasing partner states (EEPS). These EEPS reveal a mechanism that describes how to disentangle two subspaces of a Hilbert space by exciting additional states. We demonstrate this general finding in Anderson and many-body localized models. The studied concept of entanglement erasure further enables us to derive the EE of Slater determinants in the free tight binding model. Here, our analytical findings show surprisingly good agreement with numerical results of the interacting XXX chain. The described EEPS further impose a universal, i.e., model independent, erasure of EE for randomly excited Slater determinants. This feature allows us to compute many-particle EE by means of the associated single particle states and the filling ratio. This novel finding can be employed to drastically reduce the computational effort in free models.