Entanglement Entropy and Duality

Abstract

Using the algebraic approach to entanglement entropy, we study several dual pairs of lattice theories and show how the entropy is completely preserved across each duality. Our main result is that a maximal algebra of observables in a region typically dualizes to a non-maximal algebra in a dual region. In particular, we show how the usual notion of tracing out external degrees of freedom dualizes to a tracing out coupled to an additional summation over superselection sectors. We briefly comment on possible extensions of our results to more intricate dualities, including holographic ones.

20 pages; v2: typos corrected, minimal edits for clarity

References in corpus (11)

• Relative entropy equals bulk relative entropy
• Holographic representation of local bulk operators
• Causality & holographic entanglement entropy
• Bipartite entanglement and entropic boundary law in lattice spin systems
• Constructing local bulk observables in interacting AdS/CFT
• Aspects of Entanglement Entropy for Gauge Theories
• Physics at the entangling surface
• Entanglement entropy for a Maxwell field: Numerical calculation on a two dimensional lattice
• Notes on Entanglement in Abelian Gauge Theories
• Entanglement Entropy in 2D Non-abelian Pure Gauge Theory
• On the definition of entanglement entropy in lattice gauge theories

Cited by in corpus (6)

• Electromagnetic Duality and Entanglement Anomalies
• Fermionization of conformal boundary states
• On the logarithmic coefficient of the entanglement entropy of a Maxwell field
• Quantum State Reduction: Generalized Bipartitions from Algebras of Observables
• Quantum Mechanics in the Infrared
• Rényi Entropy for a $2d$ CFT with a gauge field: $\widehat{\mathrm{SU}}(\mathbf{N}{)}_1$ WZW theory on a branched torus