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:1904.12414 · Journal of Physics A Mathematical and Theoretical

Time development of conformal field theories associated with L 1 and L −1 operators

Tsukasa Tada

Published Apr 23, 2020• 16 citations
arXivHTMLPDF

Abstract

Abstract In this study, we examined consequences of unconventional time development of two-dimensional conformal field theory induced by the L 1 and L −1 operators, employing the formalism previously developed in a study of sine-square deformation. We discovered that the retainment of the Virasoro algebra requires the presence of a cut-off near the fixed points. The introduction of a scale by the cut-off makes it possible to recapture the formula for entanglement entropy in a natural and straightforward manner.

DOI
10.1088/1751-8121/ab8c63

Related papers

Analysis for Lorentzian conformal field theories through sine-square deformation

Xun Liu, Tsukasa Tada

Abstract We reexamine two-dimensional Lorentzian conformal field theory using the formalism previously developed in a study of sine-square deformation of Euclidean conformal field theory. We construct three types of Virasoro algebra. One of them reproduces the result by Lüscher and Mack, while another type exhibits divergence in the central charge term. The third leads to a continuous spectrum and contains no closed time-like curve in the system.

arXiv:2004.01930•Progress of Theoretical and Experimental Physics•May 1, 2020•9 citations

Evolution operators in conformal field theories and conformal mappings: Entanglement Hamiltonian, the sine-square deformation, and others

Xueda Wen, Shinsei Ryu, Andreas W. W. Ludwig

By making use of conformal mapping, we construct various time-evolution operators in (1+1)-dimensional conformal field theories (CFTs), which take the form $\ensuremath{\int}dx\phantom{\rule{0.16em}{0ex}}f(x)\mathcal{H}(x)$, where $\mathcal{H}(x)$ is the Hamiltonian density of the CFT and $f(x)$ is an envelope function. Examples of such deformed evolution operators include the entanglement Hamiltonian and the so-called sine-square deformation of the CFT. Within our construction, the spectrum and the (finite-size) scaling of the level spacing of the deformed evolution operator are known exactly. Based on our construction, we also propose a regularized version of the sine-square deformation, which, in contrast to the original sine-square deformation, has the spectrum of the CFT defined on a spatial circle of finite circumference $L$, and for which the level spacing scales as $1/{L}^{2}$, once the circumference of the circle and the regularization parameter are suitably adjusted.

arXiv:1604.01085•Physical review. B./Physical review. B•Jun 13, 2016•83 citations

Infinite circumference limit of conformal field theory

Nobuyuki Ishibashi, Tsukasa Tada

We argue that an infinite circumference limit can be obtained in two-dimensional conformal field theory by adopting as a Hamiltonian instead of L 0 . The theory obtained has a circumference of infinite length and hence exhibits a continuous and heavily degenerated spectrum as well as the continuous Virasoro algebra. The choice of this Hamiltonian was inspired partly by the so-called sine-square deformation, which is found in the study of a certain class of quantum statistical systems. The enigmatic behavior of sine-square deformed systems such as the sharing of their vacuum states with the closed boundary systems can be understood by the appearance of an infinite circumference.

arXiv:1504.00138•Journal of Physics A Mathematical and Theoretical•Jul 16, 2015•39 citations

Entanglement and geometry from subalgebras of the Virasoro algebra

Paweł Caputa, Dongsheng Ge

Abstract In this work we study families of generalised coherent states constructed from SL(2,R) subalgebras of the Virasoro algebra in two-dimensional conformal field theories. We derive the energy density and entanglement entropy and discuss their equivalence with analogous quantities computed in locally excited states. Moreover, we analyze their dual, holographic geometries and reproduce entanglement entropies from the Ryu-Takayanagi prescription. Finally, we outline possible applications of this universal class of states to operator growth and inhomogeneous quenches.

arXiv:2211.03630•Journal of High Energy Physics•Jun 26, 2023•29 citations

Quantum dynamics in sine-square deformed conformal field theory: Quench from uniform to nonuniform conformal field theory

Xueda Wen, Jie-qiang Wu

Sine-square deformed conformal field theory has received extensive attention in both condensed matter physics and high-energy physics recently. This is due to its unusual properties, such as having a continuous Virasoro algebra. Here, the authors investigate its nonequilibrium dynamics by studying the entanglement evolution after a quantum quench. New physical effects, such as the absence of revivals in entanglement evolution, are observed in both analytical and numerical calculations. This effect could potentially be used when engineering a gapless system with cold atoms, in order to reduce finite-size effects. The work here also sheds new light on the nonequilibrium dynamics of conformal field theory in curved spacetime.

arXiv:1802.07765•Physical review. B./Physical review. B•May 31, 2018•72 citations

Pseudoentropy for descendant operators in two-dimensional conformal field theories

Song He, Jie Yang, Yu-Xuan Zhang +1 more

We study the late-time behaviors of pseudo-(Rényi) entropy of locally excited states in rational conformal field theories. To construct the transition matrix, we utilize two nonorthogonal locally excited states that are created by the application of different descendant operators to vacuum. We show that when two descendant operators are generated by a single Virasoro generator acting on the same primary operator, the late-time excess of pseudoentropy and pseudo-Rényi entropy corresponds to the logarithm of the quantum dimension of the associated primary operator, in agreement with the case of entanglement entropy. However, for linear combination operators generated by the generic summation of Virasoro generators, we obtain a distinct late-time excess formula for the pseudo-(Rényi) entropy compared to that for (Rényi) entanglement entropy. As the mixing of holomorphic and antiholomorphic generators enhances the entanglement, in this case, the pseudo-(Rényi) entropy can receive an additional contribution. The additional contribution can be expressed as the pseudo-(Rényi) entropy of an effective transition matrix in a finite-dimensional Hilbert space.

arXiv:2301.04891•Physical review. D/Physical review. D.•Jan 30, 2024•16 citations
Abstract In this study, we examined consequences of unconventional time development of two-dimensional conformal field theory induced by the L 1 and L −1 operators, employing the formalism previously developed in a study of sine-square deformation. We discovered that the retainment of the Virasoro algebra requires the presence of a cut-off near the fixed points. The introduction of a scale by the cut-off makes it possible to recapture the formula for entanglement entropy in a natural and straightforward manner.
By making use of conformal mapping, we construct various time-evolution operators in (1+1)-dimensional conformal field theories (CFTs), which take the form $\ensuremath{\int}dx\phantom{\rule{0.16em}{0ex}}f(x)\mathcal{H}(x)$, where H(x)\mathcal{H}(x)H(x) is the Hamiltonian density of the CFT and f(x)f(x)f(x) is an envelope function. Examples of such deformed evolution operators include the entanglement Hamiltonian and the so-called sine-square deformation of the CFT. Within our construction, the spectrum and the (finite-size) scaling of the level spacing of the deformed evolution operator are known exactly. Based on our construction, we also propose a regularized version of the sine-square deformation, which, in contrast to the original sine-square deformation, has the spectrum of the CFT defined on a spatial circle of finite circumference LLL, and for which the level spacing scales as 1/L21/{L}^{2}1/L2, once the circumference of the circle and the regularization parameter are suitably adjusted.
We argue that an infinite circumference limit can be obtained in two-dimensional conformal field theory by adopting as a Hamiltonian instead of L 0 . The theory obtained has a circumference of infinite length and hence exhibits a continuous and heavily degenerated spectrum as well as the continuous Virasoro algebra. The choice of this Hamiltonian was inspired partly by the so-called sine-square deformation, which is found in the study of a certain class of quantum statistical systems. The enigmatic behavior of sine-square deformed systems such as the sharing of their vacuum states with the closed boundary systems can be understood by the appearance of an infinite circumference.
Abstract In this work we study families of generalised coherent states constructed from SL(2,R) subalgebras of the Virasoro algebra in two-dimensional conformal field theories. We derive the energy density and entanglement entropy and discuss their equivalence with analogous quantities computed in locally excited states. Moreover, we analyze their dual, holographic geometries and reproduce entanglement entropies from the Ryu-Takayanagi prescription. Finally, we outline possible applications of this universal class of states to operator growth and inhomogeneous quenches.
Sine-square deformed conformal field theory has received extensive attention in both condensed matter physics and high-energy physics recently. This is due to its unusual properties, such as having a continuous Virasoro algebra. Here, the authors investigate its nonequilibrium dynamics by studying the entanglement evolution after a quantum quench. New physical effects, such as the absence of revivals in entanglement evolution, are observed in both analytical and numerical calculations. This effect could potentially be used when engineering a gapless system with cold atoms, in order to reduce finite-size effects. The work here also sheds new light on the nonequilibrium dynamics of conformal field theory in curved spacetime.
We study the late-time behaviors of pseudo-(Rényi) entropy of locally excited states in rational conformal field theories. To construct the transition matrix, we utilize two nonorthogonal locally excited states that are created by the application of different descendant operators to vacuum. We show that when two descendant operators are generated by a single Virasoro generator acting on the same primary operator, the late-time excess of pseudoentropy and pseudo-Rényi entropy corresponds to the logarithm of the quantum dimension of the associated primary operator, in agreement with the case of entanglement entropy. However, for linear combination operators generated by the generic summation of Virasoro generators, we obtain a distinct late-time excess formula for the pseudo-(Rényi) entropy compared to that for (Rényi) entanglement entropy. As the mixing of holomorphic and antiholomorphic generators enhances the entanglement, in this case, the pseudo-(Rényi) entropy can receive an additional contribution. The additional contribution can be expressed as the pseudo-(Rényi) entropy of an effective transition matrix in a finite-dimensional Hilbert space.