TY - JOUR

T1 - Evolution operators in conformal field theories and conformal mappings

T2 - Entanglement Hamiltonian, the sine-square deformation, and others

AU - Wen, Xueda

AU - Ryu, Shinsei

AU - Ludwig, Andreas W.W.

N1 - Funding Information:
This work is supported by the NSF under Grants No. DMR-1455296 (X.W. and S.R.), No. NSF PHY11-25915, and No. DMR-1309667 (A.W.W.L.), as well as by the Alfred P. Sloan Foundation.
Publisher Copyright:
© 2016 American Physical Society.

PY - 2016/6/13

Y1 - 2016/6/13

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevB.93.235119

DO - 10.1103/PhysRevB.93.235119

M3 - Article

AN - SCOPUS:84974806677

VL - 93

JO - Physical Review B

JF - Physical Review B

SN - 2469-9950

IS - 23

M1 - 235119

ER -