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:1701.00688 · Physical review. D/Physical review. D.

Aharonov-Bohm effect on entanglement entropy in conformal field theory

Noburo Shiba

Published Sep 22, 2017• 9 citations
arXivHTMLPDF

Abstract

We consider the Aharonov-Bohm effect on entanglement entropy for one interval in ($1+1$) dimensional conformal field theory on a one dimensional ring. The magnetic field is confined inside the ring, i.e., there is a Wilson loop on the ring. The Aharonov-Bohm phase factor which is proportional to the Wilson loop is represented as insertion of twist operators. We compute exactly the R\'enyi entropy from a four point function of twist operators in a free charged scalar field.

DOI
10.1103/physrevd.96.065016

Related papers

On one-loop entanglement entropy of two short intervals from OPE of twist operators

Zhibin Li, Jiaju Zhang

We investigate the one-loop entanglement entropy of two short intervals with small cross ratio x on a complex plane in two-dimensional conformal field theory (CFT) using operator product expansion of twist operators. We focus on the one-loop entanglement entropy instead of the general order n Rényi entropy, and this makes the calculation much easier. We consider the contributions of stress tensor to order x 10, contributions of W 3 operator to order x 12, and contributions of W 4 operator to order x 14. The CFT results agree with the ones in gravity.

arXiv:1604.02779•Journal of High Energy Physics•May 1, 2016•23 citations

Entanglement entropy as a witness of the Aharonov-Bohm effect in QFT

Raúl Arias, David Blanco, Horacio Casini

We study the dependence of the entanglement entropy with a magnetic flux and show that the former quantity witnesses an Aharonov–Bohm-like effect. In particular, we consider free charged scalar and Dirac fields living on a two-dimensional cylinder and study how the entanglement entropy for a strip-like region on the surface of the cylinder is affected by a magnetic field enclosed by it.

•Mar 18, 2015•8 citations

Entanglement entropy as a witness of the Aharonov–Bohm effect in QFT

Raúl E Arias, David D Blanco, Horacio Casini

We study the dependence of the entanglement entropy with a magnetic flux and show that the former quantity witnesses an Aharonov–Bohm-like effect. In particular, we consider free charged scalar and Dirac fields living on a two-dimensional cylinder and study how the entanglement entropy for a strip-like region on the surface of the cylinder is affected by a magnetic field enclosed by it.

arXiv:1409.3269•Journal of Physics A Mathematical and Theoretical•Mar 18, 2015•6 citations

Entanglement entropy of two disjoint intervals and the recursion formula for conformal blocks

Paola Ruggiero, Erik Tonni C, Pasquale Calabrese

Abstract We reconsider the computation of the entanglement entropy of two disjoint intervals in a (1+1) dimensional conformal field theory by conformal block expansion of the 4-point correlation function of twist fields. We show that accurate results may be obtained by taking into account several terms in the operator product expansion of twist fields and by iterating the Zamolodchikov recursion formula for each conformal block. We perform a detailed analysis for the Ising conformal field theory and for the free compactified boson. Each term in the conformal block expansion can be easily analytically continued and so this approach also provides a good approximation for the von Neumann entropy.

arXiv:1805.05975•Journal of Statistical Mechanics Theory and Experiment•Nov 1, 2018•66 citations

Entanglement entropy of non-unitary conformal field theory

D Bianchini, Olalla A. Castro-Alvaredo, B Doyon +2 more

Here we show that the Rényi entanglement entropy of a region of large size ℓ in a one-dimensional critical model whose ground state breaks conformal invariance (such as in those described by non-unitary conformal field theories), behaves as , where is the effective central charge, c (which may be negative) is the central charge of the conformal field theory and is the lowest holomorphic conformal dimension in the theory. We also obtain results for models with boundaries, and with a large but finite correlation length, and we show that if the lowest conformal eigenspace is logarithmic ( with N nilpotent), then there is an additional term proportional to . These results generalize the well known expressions for unitary models. We provide a general proof, and report on numerical evidence for a non-unitary spin chain and an analytical computation using the corner transfer matrix method for a non-unitary lattice model. We use a new algebraic technique for studying the branching that arises within the replica approach, and find a new expression for the entanglement entropy in terms of correlation functions of twist fields for non-unitary models.

arXiv:1405.2804•Journal of Physics A Mathematical and Theoretical•Dec 24, 2014•113 citations

Entanglement entropy of non-unitary integrable quantum field theory

Davide Bianchini, Olalla A. Castro-Alvaredo, Benjamin Doyon

In this paper we study the simplest massive 1+1 dimensional integrable quantum field theory which can be described as a perturbation of a non-unitary minimal conformal field theory: the Lee-Yang model. We are particularly interested in the features of the bi-partite entanglement entropy for this model and on building blocks thereof, namely twist field form factors. Non-unitarity selects out a new type of twist field as the operator whose two-point function (appropriately normalized) yields the entanglement entropy. We compute this two-point function both from a form factor expansion and by means of perturbed conformal field theory. We find good agreement with CFT predictions put forward in a recent work involving the present authors. In particular, our results are consistent with a scaling of the entanglement entropy given by $\frac{c_{\text{eff}}}{3}\log \ell$ where $c_{\text{eff}}$ is the effective central charge of the theory (a positive number related to the central charge) and $\ell$ is the size of the region. Furthermore the form factor expansion of twist fields allows us to explore the large region limit of the entanglement entropy and find the next-to-leading order correction to saturation. We find that this correction is very different from its counterpart in unitary models. Whereas in the latter case, it had a form depending only on few parameters of the model (the particle spectrum), it appears to be much more model-dependent for non-unitary models.

arXiv:1502.03275•Nuclear Physics B•May 14, 2015•45 citations
We consider the Aharonov-Bohm effect on entanglement entropy for one interval in (1+11+11+1) dimensional conformal field theory on a one dimensional ring. The magnetic field is confined inside the ring, i.e., there is a Wilson loop on the ring. The Aharonov-Bohm phase factor which is proportional to the Wilson loop is represented as insertion of twist operators. We compute exactly the R'enyi entropy from a four point function of twist operators in a free charged scalar field.
We investigate the one-loop entanglement entropy of two short intervals with small cross ratio x on a complex plane in two-dimensional conformal field theory (CFT) using operator product expansion of twist operators. We focus on the one-loop entanglement entropy instead of the general order n Rényi entropy, and this makes the calculation much easier. We consider the contributions of stress tensor to order x 10, contributions of W 3 operator to order x 12, and contributions of W 4 operator to order x 14. The CFT results agree with the ones in gravity.
Abstract We reconsider the computation of the entanglement entropy of two disjoint intervals in a (1+1) dimensional conformal field theory by conformal block expansion of the 4-point correlation function of twist fields. We show that accurate results may be obtained by taking into account several terms in the operator product expansion of twist fields and by iterating the Zamolodchikov recursion formula for each conformal block. We perform a detailed analysis for the Ising conformal field theory and for the free compactified boson. Each term in the conformal block expansion can be easily analytically continued and so this approach also provides a good approximation for the von Neumann entropy.
Here we show that the Rényi entanglement entropy of a region of large size ℓ in a one-dimensional critical model whose ground state breaks conformal invariance (such as in those described by non-unitary conformal field theories), behaves as , where is the effective central charge, c (which may be negative) is the central charge of the conformal field theory and is the lowest holomorphic conformal dimension in the theory. We also obtain results for models with boundaries, and with a large but finite correlation length, and we show that if the lowest conformal eigenspace is logarithmic ( with N nilpotent), then there is an additional term proportional to . These results generalize the well known expressions for unitary models. We provide a general proof, and report on numerical evidence for a non-unitary spin chain and an analytical computation using the corner transfer matrix method for a non-unitary lattice model. We use a new algebraic technique for studying the branching that arises within the replica approach, and find a new expression for the entanglement entropy in terms of correlation functions of twist fields for non-unitary models.
In this paper we study the simplest massive 1+1 dimensional integrable quantum field theory which can be described as a perturbation of a non-unitary minimal conformal field theory: the Lee-Yang model. We are particularly interested in the features of the bi-partite entanglement entropy for this model and on building blocks thereof, namely twist field form factors. Non-unitarity selects out a new type of twist field as the operator whose two-point function (appropriately normalized) yields the entanglement entropy. We compute this two-point function both from a form factor expansion and by means of perturbed conformal field theory. We find good agreement with CFT predictions put forward in a recent work involving the present authors. In particular, our results are consistent with a scaling of the entanglement entropy given by ceff3log⁡ℓ\frac{c_{\text{eff}}}{3}\log \ell3ceff​​logℓ where ceffc_{\text{eff}}ceff​ is the effective central charge of the theory (a positive number related to the central charge) and ℓ\ellℓ is the size of the region. Furthermore the form factor expansion of twist fields allows us to explore the large region limit of the entanglement entropy and find the next-to-leading order correction to saturation. We find that this correction is very different from its counterpart in unitary models. Whereas in the latter case, it had a form depending only on few parameters of the model (the particle spectrum), it appears to be much more model-dependent for non-unitary models.