Unusual corrections to scaling in entanglement entropy

By J. Cardy, Pasquale Calabrese. 2010

157 citations recorded by the source corpus.

We present a general theory of the corrections to the asymptotic behaviour of the Rényi entropies SA(n) = (1 − n) − 1logTrρAn which measure the entanglement of an interval A of length with the rest of an infinite one-dimensional system, in the case when this is described by a conformal field theory of central charge c. These can be due to bulk irrelevant operators of scaling dimension x > 2, in which case the leading corrections are of the expected form for values of n close to 1. However, for n > x/(x − 2) corrections of the form and arise and dominate the conventional terms. We also point out that the last type of corrections can also occur with x less than 2. They arise from relevant operators induced by the conical spacetime singularities necessary to describe the reduced density matrix. These agree with recent analytic and numerical results for quantum spin chains. We also compute the effect of marginally irrelevant bulk operators, which give a correction , with a universal amplitude. We present analogous results for the case when the interval lies at the end of a semi-infinite system.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/df62d0becf06839a07158f68a242ce86bdedb33a

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In Artificial Intelligence

1. E. Tonni
2. R. Myers
3. Pasquale Calabrese
4. J. Cardy
5. M. Smolkin
6. Ling-Yan Hung
7. T. Takayanagi
8. R. Bonsignori

In Atomic and Molecular Physics, and Optics

1. R. Myers
2. E. Tonni
3. Pasquale Calabrese
4. J. Cardy
5. T. Takayanagi
6. Ling-Yan Hung
7. M. Smolkin
8. T. Faulkner

In Statistical and Nonlinear Physics

1. R. Myers
2. Ling-Yan Hung
3. M. Smolkin
4. E. Tonni
5. Pasquale Calabrese
6. J. Cardy
7. T. Takayanagi
8. R. Bonsignori

Citations in the corpus

• Entanglement negativity in extended systems: a field theoretical approach (2012, background): “The corrections to the scaling are smaller than the ones for n ≥ 2, in agreement with the general analysis of the Rényi entropies [64, 65, 68].”
• Symmetry resolved entanglement in free fermionic systems (2019, background): “[46, 47] to understand how this new universal exponent (equal to 2/n(1± α/π) for free fermions) can be obtained in CFT.”
• Some calculable contributions to holographic entanglement entropy (2011, result): “We might compare this feature of our calculations to a similar result in [37].”