Universal scaling of Klein bottle entropy near conformal critical points

TL;DR

This paper demonstrates that Klein bottle entropy near conformal critical points universally scales with the coupling constant, enabling extraction of scaling dimensions through data collapse, validated by numerical simulations of specific CFTs.

Contribution

It introduces the universal scaling behavior of Klein bottle entropy near criticality and applies it to extract scaling dimensions in lattice models.

Findings

Klein bottle entropy exhibits universal scaling near critical points.

The method accurately extracts scaling dimensions from numerical data.

Validated with Ising and Z3 parafermion CFTs using matrix product simulations.

Abstract

We show that the Klein bottle entropy [Phys. Rev. Lett. 119, 261603 (2017)] for conformal field theories (CFTs) perturbed by a relevant operator is a universal function of the dimensionless coupling constant. The universal scaling of the Klein bottle entropy near criticality provides an efficient approach to extract the scaling dimension of lattice operators via data collapse. As paradigmatic examples, we validate the universal scaling of the Klein bottle entropy for Ising and Z3 parafermion CFTs with various perturbations using numerical simulation with continuous matrix product operator approach.