Klein Bottle Partition Function and Tensor Networks in 2D Conformal Critical Theories

Explore the intersection of Klein bottle partition functions and tensor networks in characterizing 2D conformal critical theories and their adjacent phases in this hour-long lecture. Delve into the concept of Klein bottle entropy, a universal entropy exhibited by the Klein bottle partition function at conformal critical points, and its utility in characterizing critical theories in lattice models. Examine how the Klein bottle entropy transforms into a universal scaling function when the system is perturbed away from a conformal critical point, allowing for the determination of scaling dimensions of perturbation operators through data collapse. Gain insights into the application of these results in tensor network numerics and review several benchmark examples to solidify understanding.

Hong-Hao Tu: Klein bottle partition function and tensor networks