arXiv:1012.1548

Entanglement entropy for odd spheres

J. S. Dowker

Published Dec 7, 2010• 30 citations

Abstract

It is shown, non--rigorously, that the effective action on a Z_q factored odd spheres (lune) has a vanishing derivative at q=1. This leaves the effective action on the ordinary odd d-sphere as (minus) the value of the entanglement entropy associated with a (d-2)-sphere. Some numbers are given.

DOI: 10.48550/arxiv.1012.1548

Related papers

Sphere Rényi entropies

J. S. Dowker

arXiv:1212.2098Journal of Physics A Mathematical and TheoreticalMay 13, 201313 citations

Hyperspherical entanglement entropy

J. S. Dowker

arXiv:1007.3865Journal of Physics A Mathematical and TheoreticalOct 11, 201023 citations

Entanglement Entropy with Lifshitz Fermions

Dion M. F. Hartmann, Kevin Kavanagh, Stefan Vandoren +4 more

Aug 17, 20216 citations

Entanglement entropy with Lifshitz fermions

Dion M. F. Hartmann, Kevin Kavanagh, Stefan Vandoren

arXiv:2104.10913SciPost PhysicsAug 17, 20218 citations

Entanglement entropy in generalised quantum Lifshitz models

J. Angel-Ramelli, Valentina Giangreco M. Puletti, Lárus Thorlacius A

arXiv:1906.08252Journal of High Energy PhysicsAug 1, 201922 citations

Entanglement entropy and $C_T$ for monodromy defects of fields on odd-dimensional spheres

J. S. Dowker

arXiv:2201.13358Jan 31, 20220 citations

arXiv:1012.1548

Entanglement entropy for odd spheres

J. S. Dowker

Published Dec 7, 2010• 30 citations

arXiv HTML PDF

Abstract

DOI: 10.48550/arxiv.1012.1548

Related papers

Sphere Rényi entropies

J. S. Dowker

I give some scalar field theory calculations on a d -dimensional lune of arbitrary angle, evaluating, numerically, the effective action which is expressed as a simple quadrature, for conformal coupling. Using this, the entanglement and Rényi entropies are computed. Massive fields are also considered and a renormalization to make the (one-loop) effective action vanish for infinite mass is suggested and used, not entirely successfully. However a universal coefficient is derived from the large mass expansion. From the deformation of the corresponding lune result, I conjecture that the effective action on all odd manifolds with a simple conical singularity has an extremum when the singularity disappears. For the round sphere, I show how to convert the quadrature form of the conformal Laplacian determinant into the more usual sum of Riemann ζ-functions (and log 2).I give some scalar field theory calculations on a d -dimensional lune of arbitrary angle, evaluating, numerically, the effective action which is expressed as a simple quadrature, for conformal coupling. Using this, the entanglement and Rényi entropies are computed. Massive fields are also considered and a renormalization to make the (one-loop) effective action vanish for infinite mass is suggested and used, not entirely successfully. However a universal coefficient is derived from the large mass expansion. From the deformation of the corresponding lune result, I conjecture that the effective action on all odd manifolds with a simple conical singularity has an extremum when the singularity disappears. For the round sphere, I show how to convert the quadrature form of the conformal Laplacian determinant into the more usual sum of Riemann ζ-functions (and log 2).

arXiv:1212.2098Journal of Physics A Mathematical and TheoreticalMay 13, 201313 citations

Hyperspherical entanglement entropy

J. S. Dowker

The coefficient of the log term in the entanglement entropy associated with hyperspherical surfaces in flat spacetime is shown to equal the conformal anomaly by conformally transforming Euclideanized spacetime to a sphere and using already existing formulae for the relevant heat-kernel coefficients after cyclic factoring. The result follows from the fact that the conformal anomaly on this lune has an extremum at the ordinary sphere limit. A proof is given. Agreement with a recent evaluation of the coefficient is found.The coefficient of the log term in the entanglement entropy associated with hyperspherical surfaces in flat spacetime is shown to equal the conformal anomaly by conformally transforming Euclideanized spacetime to a sphere and using already existing formulae for the relevant heat-kernel coefficients after cyclic factoring. The result follows from the fact that the conformal anomaly on this lune has an extremum at the ordinary sphere limit. A proof is given. Agreement with a recent evaluation of the coefficient is found.

arXiv:1007.3865Journal of Physics A Mathematical and TheoreticalOct 11, 201023 citations

Entanglement Entropy with Lifshitz Fermions

Dion M. F. Hartmann, Kevin Kavanagh, Stefan Vandoren +4 more

We investigate fermions with Lifshitz scaling symmetry and study their entanglement entropy in 1+1 dimensions as a function of the scaling exponent $z$ . Remarkably, in the ground state the entanglement entropy vanishes for even values of $z$ , whereas for odd values it is independent of $z$ and equal to the relativistic case with $z=1$ . We show this using the correlation method on the lattice, and also using a holographic cMERA approach. The entanglement entropy in a thermal state is a more detailed function of $z$ and $T$ which we plot using the lattice correlation method. The dependence on the even- or oddness of $z$ still shows for small temperatures, but is washed out for large temperatures or large values of $z$ .We investigate fermions with Lifshitz scaling symmetry and study their entanglement entropy in 1+1 dimensions as a function of the scaling exponent $z$. Remarkably, in the ground state the entanglement entropy vanishes for even values of $z$, whereas for odd values it is independent of $z$ and equal to the relativistic case with $z=1$. We show this using the correlation method on the lattice, and also using a holographic cMERA approach. The entanglement entropy in a thermal state is a more detailed function of $z$ and $T$ which we plot using the lattice correlation method. The dependence on the even- or oddness of $z$ still shows for small temperatures, but is washed out for large temperatures or large values of $z$.

Aug 17, 20216 citations

Entanglement entropy with Lifshitz fermions

Dion M. F. Hartmann, Kevin Kavanagh, Stefan Vandoren

We investigate fermions with Lifshitz scaling symmetry and study their entanglement entropy in 1+1 dimensions as a function of the scaling exponent z. Remarkably, in the ground state the entanglement entropy vanishes for even values of z, whereas for odd values it is independent of z and equal to the relativistic case with z=1. We show this using the correlation method on the lattice, and also using a holographic cMERA approach. The entanglement entropy in a thermal state is a more detailed function of z and T which we plot using the lattice correlation method. The dependence on the even- or oddness of z still shows for small temperatures, but is washed out for large temperatures or large values of z.We investigate fermions with Lifshitz scaling symmetry and study their entanglement entropy in 1+1 dimensions as a function of the scaling exponent z. Remarkably, in the ground state the entanglement entropy vanishes for even values of z, whereas for odd values it is independent of z and equal to the relativistic case with z=1. We show this using the correlation method on the lattice, and also using a holographic cMERA approach. The entanglement entropy in a thermal state is a more detailed function of z and T which we plot using the lattice correlation method. The dependence on the even- or oddness of z still shows for small temperatures, but is washed out for large temperatures or large values of z.

arXiv:2104.10913SciPost PhysicsAug 17, 20218 citations

Entanglement entropy in generalised quantum Lifshitz models

J. Angel-Ramelli, Valentina Giangreco M. Puletti, Lárus Thorlacius A

Abstract We compute universal finite corrections to entanglement entropy for generalised quantum Lifshitz models in arbitrary odd spacetime dimensions. These are generalised free field theories with Lifshitz scaling symmetry, where the dynamical critical exponent z equals the number of spatial dimensions d, and which generalise the 2+1-dimensional quantum Lifshitz model to higher dimensions. We analyse two cases: one where the spatial manifold is a d-dimensional sphere and the entanglement entropy is evaluated for a hemisphere, and another where a d-dimensional flat torus is divided into two cylinders. In both examples the finite universal terms in the entanglement entropy are scale invariant and depend on the compactification radius of the scalar field.Abstract We compute universal finite corrections to entanglement entropy for generalised quantum Lifshitz models in arbitrary odd spacetime dimensions. These are generalised free field theories with Lifshitz scaling symmetry, where the dynamical critical exponent z equals the number of spatial dimensions d, and which generalise the 2+1-dimensional quantum Lifshitz model to higher dimensions. We analyse two cases: one where the spatial manifold is a d-dimensional sphere and the entanglement entropy is evaluated for a hemisphere, and another where a d-dimensional flat torus is divided into two cylinders. In both examples the finite universal terms in the entanglement entropy are scale invariant and depend on the compactification radius of the scalar field.

arXiv:1906.08252Journal of High Energy PhysicsAug 1, 201922 citations

Entanglement entropy and $C_T$ for monodromy defects of fields on odd-dimensional spheresEntanglement entropy and $C_T$ for monodromy defects of fields on odd-dimensional spheres

J. S. Dowker

The effect of a spherical monodromy defect on the entanglement entropy and central charge $C_T$ of a free conformal scalar field propagating on an odd-dimensional sphere is investigated. As on even spheres the central charge becomes negative for a range of the flux parameter, $δ$ , with possible implications for reflection positivity. The work is mostly numerical but closed forms are found for the $Z_2$ monodromy ( $δ=1/2$ ) yielding an explicit $d\to\infty$ limit, $C_T\to -6/π$ The effect of a spherical monodromy defect on the entanglement entropy and central charge $C_T$ of a free conformal scalar field propagating on an odd-dimensional sphere is investigated. As on even spheres the central charge becomes negative for a range of the flux parameter, $δ$, with possible implications for reflection positivity. The work is mostly numerical but closed forms are found for the $Z_2$ monodromy ($δ=1/2$) yielding an explicit $d\to\infty$ limit, $C_T\to -6/π$

arXiv:2201.13358Jan 31, 20220 citations

We investigate fermions with Lifshitz scaling symmetry and study their entanglement entropy in 1+1 dimensions as a function of the scaling exponent

z

. Remarkably, in the ground state the entanglement entropy vanishes for even values of

z

, whereas for odd values it is independent of

z

and equal to the relativistic case with

z=1

. We show this using the correlation method on the lattice, and also using a holographic cMERA approach. The entanglement entropy in a thermal state is a more detailed function of

z

and

T

which we plot using the lattice correlation method. The dependence on the even- or oddness of

z

still shows for small temperatures, but is washed out for large temperatures or large values of

z

Entanglement entropy and

C_T

for monodromy defects of fields on odd-dimensional spheres

The effect of a spherical monodromy defect on the entanglement entropy and central charge

C_T

of a free conformal scalar field propagating on an odd-dimensional sphere is investigated. As on even spheres the central charge becomes negative for a range of the flux parameter,

δ

, with possible implications for reflection positivity. The work is mostly numerical but closed forms are found for the

Z_2

monodromy (

δ=1/2

) yielding an explicit

d\to\infty

limit,

C_T\to -6/π