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How robust is the entanglement entropy-area relation?
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We revisit the problem of finding the entanglement entropy of a scalar field on a lattice by tracing over its degrees of freedom inside a sphere. It is known that this entropy satisfies the area law -- entropy proportional to the area of the sphere -- when the field is assumed to be in its ground state. We show that the area law continues to hold when the scalar field degrees of freedom are in generic coherent states and a class of squeezed states. However, when excited states are considered, the entropy scales as a lower power of the area. This suggests that for large horizons, the ground state entropy dominates, whereas entropy due to excited states gives power law corrections. We discuss possible implications of this result to black hole entropy.
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Cited by 2 Pith papers
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Entanglement Entropy of Quantum Corners
For a two-dimensional corner symmetry algebra, coherent corner states give an entanglement entropy that scales with the area when mapped to near-extremal Reissner-Nordström black holes.
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Entanglement entropy and $T\bar T$ deformations beyond antipodal points from holography
For a holographic (A)dS spacetime with a hard radial cutoff, the entanglement entropy of any interval on the sphere equals the antipodal-point formula with radius R cos(beta_epsilon).
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