Comments on Rényi entropy in AdS3/CFT2

Abstract:In this work, we study the universal behaviors in the mutual information of two disjoint spheres in a conformal field theory (CFT). By using the operator product expansion of the spherical twist operator in terms of the conformal family, we show that the large distance expansion of the mutual information can be cast in terms of the conformal blocks. We develop the 1/n prescription to compute the coefficients before the conformal blocks. For a single conformal family, the leading nonvanishing contribution to the mutual information comes from the bilinear operators. We show that the coefficients of these operators take universal forms and such universal behavior persists in the bilinear operators with derivatives as well. Consequently the first few leading order contributions to the mutual information in CFT take universal forms. To illustrate our framework, we discuss the free scalars and free fermions in various dimensions. For the free scalars, we compute the mutual information to the next-to-leading order and find good agreement with the improved numerical lattice result. For the free fermion, we compute the leading order result, which is of universal form, and find the good match with the numerical study. Our formalism could be applied to any CFT potentially.

Section: Jhep06(2017)096mentioning

confidence: 99%

On the mutual information in conformal field theory

Chen

Hao

et al. 2017

“…After that, one can obtain the short-interval expansion of the Rényi entropy by evaluating the corresponding one-point or multi-point functions of the OPE blocks. This trick has been adopted to calculate the Rényi entropy for some special cases [11][12][13][14][15][16][17][18][19][20], such as the Rényi entropy of two intervals on complex plane and of the one-interval on torus. In this paper, we adopt the same trick to investigate the short-interval expansion of excited state Rényi entropy on a cylinder, and then compare our results with the thermal state Rényi entropy.…”

Section: Jhep11(2016)116mentioning

confidence: 99%

Thermality and excited state Rényi entropy in two-dimensional CFT

Lin

Wang

Zhang

2016

We evaluate one-interval Rényi entropy and entanglement entropy for the excited states of two-dimensional conformal field theory (CFT) on a cylinder, and examine their differences from the ones for the thermal state. We assume the interval to be short so that we can use operator product expansion (OPE) of twist operators to calculate Rényi entropy in terms of sum of one-point functions of OPE blocks. We find that the entanglement entropy for highly excited state and thermal state behave the same way after appropriate identification of the conformal weight of the state with the temperature. However, there exists no such universal identification for the Rényi entropy in the short-interval expansion. Therefore, the highly excited state does not look thermal when comparing its Rényi entropy to the thermal state one. As the Rényi entropy captures the higher moments of the reduced density matrix but the entanglement entropy only the average, our results imply that the emergence of thermality depends on how refined we look into the entanglement structure of the underlying pure excited state.

“…the spectrum of the operators and the OPE coefficients [20] (see also [21][22][23][24] and for related work [25][26][27][28][29]). One may ask whether a similar approach can be useful in the computation of entanglement negativity, and if the holographic prescription can be inferred from it.…”

Section: Jhep09(2014)010mentioning

confidence: 99%

Conformal blocks and negativity at large central charge

Kulaxizi

Parnachev

Policastro

2014

141

We consider entanglement negativity for two disjoint intervals in 1+1 dimensional CFT in the limit of large central charge. As the two intervals get close, the leading behavior of negativity is given by the logarithm of the conformal block where a set of approximately null descendants appears in the intermediate channel. We compute this quantity numerically and compare with existing analytic methods which provide perturbative expansion in powers of the cross-ratio.