Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1511.01330 · Physical review. D/Physical review. D.

Entanglement entropy on fractals

Amin Faraji Astaneh

Published Mar 16, 2016• 4 citations
arXivHTMLPDF

Abstract

We use the heat kernel method to calculate the entanglement entropy for a given entangling region on a fractal. The leading divergent term of the entropy is obtained as a function of the fractal dimension as well as the walk dimension. The power of the UV cutoff parameter is (generally) a fractional number, which, indeed, is a certain combination of these two indices. This exponent is known as the spectral dimension. We show that there is a novel log-periodic oscillatory behavior in the expression of entropy which has root in the complex dimension of the fractal. We finally indicate that the holographic calculation in a certain hyperscaling-violating bulk geometry yields the same leading term for the entanglement entropy, if one identifies the effective dimension of the hyperscaling-violating theory with the spectral dimension of the fractal. We provide additional support by comparing the behavior of the thermal entropy in terms of the temperature, computed for two geometries, the fractal geometry and the hyperscaling-violating background.

DOI
10.1103/physrevd.93.066004

Related papers

Aspects of holographic entanglement entropy: shape dependence and hyperscaling violating backgrounds

Piermarco Fonda

This thesis collects three works about holographic computations of entanglement entropy. In the first one it is shown how to compute numerically, following the Ryu-Takayanagi prescription, the entanglement entropy for arbitrarily shaped entangling regions in three dimensional conformal field theories. The other two focus on holographic theories with hyperscaling violating exponents: the time dependence after a holographic quench is analyzed and the arising of new universal terms due to the presence of non smooth boundaries is shown.

•Jan 2, 2016•0 citations

Entanglement entropy on finitely ramified graphs

Ibrahim Akal

We compute the entanglement entropy in a composite system separated by a finitely ramified boundary with the structure of a self-similar lattice graph. We derive the entropy as a function of the decimation factor which determines the spectral dimension, the latter being generically different from the topological dimension. For large decimations, the graph becomes increasingly dense, yielding a gain in the entanglement entropy which, in the asymptotically smooth limit, approaches a constant value. Conversely, a small decimation factor decreases the entanglement entropy due to a large number of spectral gaps which regulate the amount of information crossing the boundary. In line with earlier studies, we also comment on similarities with certain holographic formulations. Finally, we calculate the higher order corrections in the entanglement entropy which possess a log-periodic oscillatory behavior.

arXiv:1808.10391•Physical review. D/Physical review. D.•Nov 5, 2018•5 citations

Bulk entanglement and its shape dependence

Zhong-Ying Fan

Abstract We study bulk entanglement entropy in even spacetime dimensions using the heat kernel method, which captures the universal piece of entanglement entropy, a logarithmically divergent term in even dimensions. In four dimensions, we perform explicit calculations for various shapes of boundary subregions. In particular, for a cusp subregion with an arbitrary opening angle, we find that the bulk entanglement entropy always encodes the same universal information about the boundary theories as the leading entanglement entropy in the large N limit, up to a fixed proportional constant. By smoothly deforming a circle in the boundary, we find that to leading order of the deformations, the bulk entanglement entropy shares the same shape dependence as the leading entanglement entropy and hence the same physical information can be extracted from both cases. This establishes an interesting local/nonlocal relation for holographic $$\mathrm {CFT}_3$$ CFT 3 . However, the result does not hold for higher dimensional holographic theories.

arXiv:2101.00194•The European Physical Journal C•Jul 1, 2021•0 citations

Entanglement entropy for singular surfaces in hyperscaling violating theories

Mohsen Alishahiha, Amin Faraji Astaneh, Piermarco Fonda +1 more

We study the holographic entanglement entropy for singular surfaces in theories described holographically by hyperscaling violating backgrounds. We consider singular surfaces consisting of cones or creases in diverse dimensions. The structure of UV divergences of entanglement entropy exhibits new logarithmic terms whose coefficients, being cut-off independent, could be used to define new central charges in the nearly smooth limit. We also show that there is a relation between these central charges and the one appearing in the two-point function of the energy-momentum tensor. Finally we examine how this relation is affected by considering higher-curvature terms in the gravitational action.

arXiv:1507.05897•Journal of High Energy Physics•Sep 1, 2015•26 citations

An analytic approach for holographic entanglement entropy at (quantum) criticality

Parul Jain, Matti Järvinen

A bstract We consider holographic entanglement entropy in AdS black hole backgrounds by using the limit of large number of dimensions. By dividing the geometry to two patches (with one patch covering the vicinity of the black hole horizon and another covering the other regions), we are able to obtain fully analytic expressions for the entropy when the entanglement region is a strip. We argue that apart from conformal field theories at finite temperature in high number of dimensions, our method works for nearly critical theories in 3+1 dimensions. In the case of extremal black holes, dual to quantum critical systems, the results take a particularly simple form. We also comment on the case of soliton geometries. Finally, we analyze entanglement entropy for wide strips, and propose a general formula for the first subleading term in the expansion of the entropy in (inverse) system size for generic entanglement regions.

arXiv:2509.25360•Journal of High Energy Physics•Mar 17, 2026•0 citations

Universal terms of holographic entanglement entropy in theories with hyperscaling violation

Mohammad Reza Tanhayi

We examine the holographic entanglement entropy in hyperscaling violating backgrounds. Precisely in such theories, by semianalytic computation, we use holographic methods to derive the universal terms of entanglement entropy in various dimensions. We also find such terms when the bulk action includes higher-order curvature terms. We make further comments on the mutual information in hyperscaling violating backgrounds with higher curvature interactions. We explore the sign of tripartite information, which results in a monogamy property on mutual information. It is shown that for various hyperscaling parameters, the mutual and tripartite information are always positive and negative, respectively. This indicates that mutual information is monogamous in theories with hyperscaling violation.

arXiv:1711.10526•Physical review. D/Physical review. D.•May 15, 2018•6 citations
We use the heat kernel method to calculate the entanglement entropy for a given entangling region on a fractal. The leading divergent term of the entropy is obtained as a function of the fractal dimension as well as the walk dimension. The power of the UV cutoff parameter is (generally) a fractional number, which, indeed, is a certain combination of these two indices. This exponent is known as the spectral dimension. We show that there is a novel log-periodic oscillatory behavior in the expression of entropy which has root in the complex dimension of the fractal. We finally indicate that the holographic calculation in a certain hyperscaling-violating bulk geometry yields the same leading term for the entanglement entropy, if one identifies the effective dimension of the hyperscaling-violating theory with the spectral dimension of the fractal. We provide additional support by comparing the behavior of the thermal entropy in terms of the temperature, computed for two geometries, the fractal geometry and the hyperscaling-violating background.
This thesis collects three works about holographic computations of entanglement entropy. In the first one it is shown how to compute numerically, following the Ryu-Takayanagi prescription, the entanglement entropy for arbitrarily shaped entangling regions in three dimensional conformal field theories. The other two focus on holographic theories with hyperscaling violating exponents: the time dependence after a holographic quench is analyzed and the arising of new universal terms due to the presence of non smooth boundaries is shown.
We compute the entanglement entropy in a composite system separated by a finitely ramified boundary with the structure of a self-similar lattice graph. We derive the entropy as a function of the decimation factor which determines the spectral dimension, the latter being generically different from the topological dimension. For large decimations, the graph becomes increasingly dense, yielding a gain in the entanglement entropy which, in the asymptotically smooth limit, approaches a constant value. Conversely, a small decimation factor decreases the entanglement entropy due to a large number of spectral gaps which regulate the amount of information crossing the boundary. In line with earlier studies, we also comment on similarities with certain holographic formulations. Finally, we calculate the higher order corrections in the entanglement entropy which possess a log-periodic oscillatory behavior.
Abstract We study bulk entanglement entropy in even spacetime dimensions using the heat kernel method, which captures the universal piece of entanglement entropy, a logarithmically divergent term in even dimensions. In four dimensions, we perform explicit calculations for various shapes of boundary subregions. In particular, for a cusp subregion with an arbitrary opening angle, we find that the bulk entanglement entropy always encodes the same universal information about the boundary theories as the leading entanglement entropy in the large N limit, up to a fixed proportional constant. By smoothly deforming a circle in the boundary, we find that to leading order of the deformations, the bulk entanglement entropy shares the same shape dependence as the leading entanglement entropy and hence the same physical information can be extracted from both cases. This establishes an interesting local/nonlocal relation for holographic CFT3\mathrm {CFT}_3CFT3​ CFT 3 . However, the result does not hold for higher dimensional holographic theories.
We study the holographic entanglement entropy for singular surfaces in theories described holographically by hyperscaling violating backgrounds. We consider singular surfaces consisting of cones or creases in diverse dimensions. The structure of UV divergences of entanglement entropy exhibits new logarithmic terms whose coefficients, being cut-off independent, could be used to define new central charges in the nearly smooth limit. We also show that there is a relation between these central charges and the one appearing in the two-point function of the energy-momentum tensor. Finally we examine how this relation is affected by considering higher-curvature terms in the gravitational action.
A bstract We consider holographic entanglement entropy in AdS black hole backgrounds by using the limit of large number of dimensions. By dividing the geometry to two patches (with one patch covering the vicinity of the black hole horizon and another covering the other regions), we are able to obtain fully analytic expressions for the entropy when the entanglement region is a strip. We argue that apart from conformal field theories at finite temperature in high number of dimensions, our method works for nearly critical theories in 3+1 dimensions. In the case of extremal black holes, dual to quantum critical systems, the results take a particularly simple form. We also comment on the case of soliton geometries. Finally, we analyze entanglement entropy for wide strips, and propose a general formula for the first subleading term in the expansion of the entropy in (inverse) system size for generic entanglement regions.
We examine the holographic entanglement entropy in hyperscaling violating backgrounds. Precisely in such theories, by semianalytic computation, we use holographic methods to derive the universal terms of entanglement entropy in various dimensions. We also find such terms when the bulk action includes higher-order curvature terms. We make further comments on the mutual information in hyperscaling violating backgrounds with higher curvature interactions. We explore the sign of tripartite information, which results in a monogamy property on mutual information. It is shown that for various hyperscaling parameters, the mutual and tripartite information are always positive and negative, respectively. This indicates that mutual information is monogamous in theories with hyperscaling violation.