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 - 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.
UR - http://www.scopus.com/inward/record.url?scp=84974806677&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84974806677&partnerID=8YFLogxK
U2 - 10.1103/PhysRevB.93.235119
DO - 10.1103/PhysRevB.93.235119
M3 - Article
AN - SCOPUS:84974806677
SN - 2469-9950
VL - 93
JO - Physical Review B
JF - Physical Review B
IS - 23
M1 - 235119
ER -