Entanglement sum rules in exactly solvable models

TL;DR

This paper demonstrates an entanglement sum rule in exactly solvable models, showing that the total entanglement entropy decomposes into additive contributions from matter and gauge fields, applicable across various quantum phases.

Contribution

It establishes an exact entanglement sum rule for a broad class of solvable models, extending previous proofs to include finite temperature and new models, and proving the additivity of Renyi entropy.

Findings

Entanglement entropy is additive in these models.

Renyi entropy factorizes, confirming spectrum additivity.

Applicable to diverse phases like Fermi liquids and spin liquids.

Abstract

We compute the entanglement entropy of a wide class of exactly solvable models which may be characterized as describing matter coupled to gauge fields. Our principle result is an entanglement sum rule which states that entropy of the full system is the sum of the entropies of the two components. In the context of the exactly solvable models we consider, this result applies to the full entropy, but more generally it is a statement about the additivity of universal terms in the entropy. We also prove that the Renyi entropy is exactly additive and hence that the entanglement spectrum factorizes. Our proof simultaneously extends and simplifies previous arguments, with extensions including new models at zero temperature as well as the ability to treat finite temperature crossovers. We emphasize that while the additivity is an exact statement, each term in the sum may still be difficult to compute. Our results apply to a wide variety of phases including Fermi liquids, spin liquids, and some non-Fermi liquid metals.