Spatially local extensions and entanglement-law characterization

Investigate how replacing the all-to-all exactly k-local spin ensemble with a spatially local one- or two-dimensional model changes the entanglement of the selected non-Hermitian eigenstate, including whether the outlier-to-bulk mechanism can produce area-law, logarithmic, and volume-law entanglement phases.

Background

The paper studies an all-to-all interacting non-Hermitian spin ensemble whose dominant eigenstate switches from a weakly entangled spectral outlier to a highly entangled bulk eigenstate when disorder increases. Because the model has no spatial structure, its entanglement properties cannot be directly interpreted in terms of conventional area-law, logarithmic, or volume-law phases.

The authors explicitly identify the role of spatial locality as unresolved and propose constructing a spatially local chaotic Hermitian Hamiltonian coupled to an anti-Hermitian component that generates an isolated outlier. Increasing the chaotic component could then induce a transition between an outlier-selected low-entanglement state and a bulk-selected highly entangled state, connecting the random-matrix mechanism to spatially extended many-body entanglement phases.