589 research outputs found
Universal Thermal Corrections to Entanglement Entropy for Conformal Field Theories on Spheres
We consider entanglement entropy of a cap-like region for a conformal field
theory living on a sphere times a circle in d space-time dimensions. Assuming
that the finite size of the system introduces a unique ground state with a
nonzero mass gap, we calculate the leading correction to the entanglement
entropy in a low temperature expansion. The correction has a universal form for
any conformal field theory that depends only on the size of the mass gap, its
degeneracy, and the angular size of the cap. We confirm our result by
calculating the entanglement entropy of a conformally coupled scalar
numerically. We argue that an apparent discrepancy for the scalar can be
explained away through a careful treatment of boundary terms. In an appendix,
to confirm the accuracy of the numerics, we study the mutual information of two
cap-like regions at zero temperature.Comment: 18 pages, 5 figures; v2, major revision, discrepancy explained
(published version); v3, beta typo fixed, refs adde
Universal Thermal Corrections to Single Interval Entanglement Entropy for Conformal Field Theories
We consider single interval R\'enyi and entanglement entropies for a two
dimensional conformal field theory on a circle at nonzero temperature. Assuming
that the finite size of the system introduces a unique ground state with a
nonzero mass gap, we calculate the leading corrections to the R\'enyi and
entanglement entropy in a low temperature expansion. These corrections have a
universal form for any two dimensional conformal field theory that depends only
on the size of the mass gap and its degeneracy. We analyze the limits where the
size of the interval becomes small and where it becomes close to the size of
the spatial circle.Comment: 5 pages, 1 figure; v2 minor clarifications added, to appear in PR
Thermal Corrections to R\'enyi entropies for Free Fermions
We calculate thermal corrections to R\'{e}nyi entropies for free massless
fermions on a sphere. More specifically, we take a free fermion on
and calculate the leading thermal correction
to the R\'{e}nyi entropies for a cap like region with opening angle .
By expanding the density matrix in a Boltzmann sum, the problem of finding the
R\'{e}nyi entropies can be mapped to the problem of calculating a two point
function on an sheeted cover of the sphere. We follow previous work for
conformal field theories to map the problem on the sphere to a conical region
in Euclidean space. By using the method of images, we calculate the two point
function and recover the R\'{e}nyi entropies.Comment: 15 pages, 5 figure
Tracing Through Scalar Entanglement
As a toy model of a gapped system, we investigate the entanglement entropy of
a massive scalar field in 1+1 dimensions at nonzero temperature. In a small
mass m and temperature T limit, we put upper and lower bounds on the two
largest eigenvalues of the covariance matrix used to compute the entanglement
entropy. We argue that the entanglement entropy has exp(-m/T) scaling in the
limit m >> T. We comment on the relation between our work and the
Ryu-Takayanagi proposal for computing the entanglement entropy holographically.Comment: 17 pages, 11 figures; v2 ref added, typos fixed; v3 refs added, minor
clarifications, version to appear in PR
Thermal Corrections to Renyi Entropies for Conformal Field Theories
We compute thermal corrections to R\'enyi entropies of dimensional
conformal field theories on spheres. Consider the th R\'enyi entropy for a
cap of opening angle on . From a Boltzmann sum
decomposition and the operator-state correspondence, the leading correction is
related to a certain two-point correlation function of the operator (not equal
to the identity) with smallest scaling dimension. More specifically, via a
conformal map, the correction can be expressed in terms of the two-point
function on a certain conical space with opening angle . In the case of
free conformal field theories, this two-point function can be computed
explicitly using the method of images. We perform the computation for the
conformally coupled scalar. From the limit of our results, we extract
the leading thermal correction to the entanglement entropy, reproducing results
of arXiv:1407.1358.Comment: 18 pages, 5 figures; v2 reference adde
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