Browsing by Author "Ryu, Shinsei"

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    Crystalline topological phases and quantum anomalies
    (2015-05) Ryu, Shinsei
    In this talk, I plan to discuss phases of matter with reflection symmetry (parity symmetry) with interactions. While a systematic analysis is possible for non-interacting fermions, an important challenge is to understand the effects of strong electron correlations. To get some insight into this problem, I will discuss an example where by the effects of interactions the non-interacting classification breaks down. I will also propose a generalization of Laughlin’ s thought experiment, a theoretical method which is powerful enough to diagnose topological phases with U(1) symmetry but no other symmetries, to the cases of various symmetry protected topological phases. For the case of parity symmetry, the proposed generalization consists of putting they boundary theories of a SPT phase on an unoriented surfaces, and hence is related to the so-called orientifold quantum field theories.
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    Sine-Square deformation of conformal field theory
    (2018-05) Ryu, Shinsei
    By making use of conformal mapping, we construct various time-evolution operators in (1+1) dimensional conformal field theories (CFTs) deformed by some envelope function. Examples of such deformed evolution operators include the entanglement Hamiltonian, and the so-called sinesquare 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.