# Entanglement area laws for long-range interacting systems

## TL;DR

This paper establishes bounds on how quickly entanglement entropy can grow in long-range interacting quantum systems and shows conditions under which ground states obey the entanglement area law, extending known results for short-range systems.

## Contribution

It proves entanglement growth bounds and area law conditions for long-range interactions, generalizing previous short-range results to systems with power-law decaying interactions.

## Key findings

- Entanglement entropy growth rate is bounded by boundary area for $oldsymbol{ ext{long-range}}$ systems.
- Ground states satisfy the area law if connected via gapped adiabatic paths for certain $oldsymbol{ ext{long-range}}$ interactions.
- Results help identify phase transitions in long-range quantum systems.

## Abstract

We prove that the entanglement entropy of any state evolved under an arbitrary $1/r^{\alpha}$ long-range-interacting D-dimensional lattice spin Hamiltonian cannot change faster than a rate proportional to the boundary area for any $\alpha>D+1$. We also prove that for any $\alpha>2D+2$, the ground state of such a Hamiltonian satisfies the entanglement area law if it can be transformed along a gapped adiabatic path into a ground state known to satisfy the area law. These results significantly generalize their existing counterparts for short-range interacting systems, and are useful for identifying dynamical phase transitions and quantum phase transitions in the presence of long-range interactions.