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

By making use of conformal mapping, we construct various time-evolution operators in (1+1)-dimensional conformal field theories (CFTs), which take the form [integraloperator]dx[functionof](x)[scriptH](x), where [scriptH](x) is the Hamiltonian density of the CFT and [functionof](x) is an envelope fun...

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Bibliographic Details
Published in:Physical review. B 2016-06, Vol.93 (23), Article 235119
Main Authors: Wen, Xueda, Ryu, Shinsei, Ludwig, Andreas W. W.
Format: Article
Language:English
Subjects:
Circumferences
Condensed matter
Construction
Deformation
Evolution
Field theory
Hamiltonian functions
Operators
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Summary:By making use of conformal mapping, we construct various time-evolution operators in (1+1)-dimensional conformal field theories (CFTs), which take the form [integraloperator]dx[functionof](x)[scriptH](x), where [scriptH](x) is the Hamiltonian density of the CFT and [functionof](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 super(2), once the circumference of the circle and the regularization parameter are suitably adjusted.
ISSN:2469-9950
2469-9969
DOI:10.1103/PhysRevB.93.235119