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

Research output: Contribution to journalArticlepeer-review

26 Scopus citations

Abstract

By making use of conformal mapping, we construct various time-evolution operators in (1+1)-dimensional conformal field theories (CFTs), which take the form ∫dxf(x)H(x), where 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/L2, once the circumference of the circle and the regularization parameter are suitably adjusted.

Original languageEnglish (US)
Article number235119
JournalPhysical Review B
Volume93
Issue number23
DOIs
StatePublished - Jun 13 2016
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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