# Nonlocal fermions and the entropy volume law

## TL;DR

This paper introduces a nonlocal fermionic model with a randomized dispersion relation that exhibits an extensive entanglement entropy volume law, contrasting with local fermions' area law, and explores its holographic dual implications.

## Contribution

It proposes a novel nonlocal fermion model with a randomized dispersion relation that produces a volume law for entanglement entropy, supported by exact diagonalizations and holographic analysis.

## Key findings

- Nonlocal fermions exhibit volume law entanglement entropy.
- The central charge relates to the locality scale in 1D.
- Holographic dual suggests a spacetime with UV and IR scales proportional to the locality scale.

## Abstract

To produce a fermionic model exhibiting an entanglement entropy volume law, we propose a particular version of nonlocality in which the energy-momentum dispersion relation is effectively randomized at the shortest length scales while preserving translation invariance. In contrast to the ground state of local fermions, exhibiting an entanglement entropy area law with logarithmic corrections, the entropy of nonlocal fermions is extensive, scaling as the volume of the subregion and crossing over to the anomalous fermion area law at scales larger than the locality scale, {\alpha}. In the 1-d case, we are able to show that the central charge appearing in the universal entropy expressions for large subregions is simply related to the locality scale. These results are demonstrated by exact diagonalizations of the corresponding discrete lattice fermion models. Within the Ryu-Takayanagi holographic picture, the relation between the central charge and the locality scale suggest a dual spacetime in which the size of the flat UV portion and the radius of AdS in the IR are both proportional to the locality scale, {\alpha}.