Entanglement sum rules in exactly solvable models

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.

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Cited by in corpus (10)

• Quantum Entanglement of Interacting Fermions in Monte Carlo
• Chiral Symmetry Breaking, Deconfinement and Entanglement Monotonicity
• Entanglement entropy of the $\nu =1/2$ composite fermion non-Fermi liquid state
• The negativity contour: a quasi-local measure of entanglement for mixed states
• Direct calculation of the Entanglement Spectrum in Quantum Monte Carlo with application to \textit{ab initio} Hamiltonians
• (A)dS Holography with a Cut-off
• Entanglement entropy of composite Fermi liquid states on the lattice: In support of the Widom formula
• Entanglement entropy of compressible holographic matter: loop corrections from bulk fermions
• Gauge field entanglement of Kitaev's honeycomb model
• Interplay between short and long-range entanglement in symmetry protected phases