We present a general theory of the corrections to the asymptotic behaviour of the Renyi entropies S(A)((n)) = (1 - n)(-1) log Tr rho(n)(A) which measure the entanglement of an interval A of length l 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 l(-2(x-2)) for values of n close to 1. However, for n > x/(x - 2) corrections of the form l(2-x-x/n) and l(-2x/n) 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 O((log l)(-2)), with a universal amplitude. We present analogous results for the case when the interval lies at the end of a semi-infinite system.

Unusual corrections to scaling in entanglement entropy

CALABRESE, PASQUALE
2010-01-01

Abstract

We present a general theory of the corrections to the asymptotic behaviour of the Renyi entropies S(A)((n)) = (1 - n)(-1) log Tr rho(n)(A) which measure the entanglement of an interval A of length l 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 l(-2(x-2)) for values of n close to 1. However, for n > x/(x - 2) corrections of the form l(2-x-x/n) and l(-2x/n) 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 O((log l)(-2)), with a universal amplitude. We present analogous results for the case when the interval lies at the end of a semi-infinite system.
2010
Cardy, J; Calabrese, Pasquale
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/139464
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