Highly entangled quantum systems in 3+1 dimensions

TL;DR

This paper discusses three 3+1 dimensional quantum systems that violate the typical boundary law for entanglement entropy, highlighting their low-energy gapless modes and implications for highly entangled quantum states.

Contribution

It introduces three distinct 3+1D systems with boundary law violations and unifies them through their low-energy gapless modes, expanding understanding of entanglement in quantum matter.

Findings

Weyl fermions in magnetic fields violate boundary law

Holographic models show similar violations at strong coupling

Topological insulators with dislocations exhibit boundary law violations

Abstract

Many systems exhibit boundary law scaling for entanglement entropy in more than one spatial dimension. Here I describe three systems in 3+1 dimensions that violate the boundary law for entanglement entropy. The first is free Weyl fermions in a magnetic field, the second is a holographic strong coupling generalization of the Weyl fermion system, and the third is a strong topological insulator in the presence of dislocations. These systems are unified by the presence of a low energy description that includes many gapless 1+1 dimensional modes. I conclude with some comments on the search for highly entangled states of quantum matter and some potential experimental signatures.