2016/04/12 by Xueda Wen, Shinsei Ryu, Andreas W. W. Ludwig · 6 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Conformal field theory #Conformal map #Conformal symmetry #Geometry #Hamiltonian (control theory) #Mathematical analysis #Mathematical physics #Mathematics #Numerical methods for differential equations #Operator (biology) #Physics #Quantum #Quantum entanglement #Quantum mechanics #Scaling #Square (algebra) #cond-mat.str-el #hep-th
paper · pdf · doi:10.1103/physrevb.93.235119
published as Phys. Rev. B 93, 235119 (2016) · 11 pages, 16 figures; (v2): The connection between the "square root deformation" and the perfect state transfer is added in v2. We thank Hosho Katsura for pointing out the connection
arxiv created 2016/04/12 · openalex publication_date 2016/06/13 · arxiv updated 2016/06/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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∫dx\phantom\rule0.16em0exf(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.