Jared Heymann | Searcharxiv

arXiv2025

Unitary and Nonunitary A-D-E minimal models: Coset graph fusion algebras, defects, entropies, SREEs and dilogarithm identities

We consider both unitary and nonunitary A-D-E minimal models on the cylinder with topological defects along the non-contractible cycle of the cylinder. We define the coset graph $A \otimes G/\mathbb{Z}_2$ and argue that it encodes not only the (i) coset graph fusion algebra, but also (ii) the Affleck-Ludwig boundary g-factors; (iii) the defect g-factors (quantum dimensions) and (iv) the relative symmetry resolved entanglement entropy. By studying A-D-E restricted solid-on-solid models, we find that these boundary conformal field theory structures are also present on the lattice: defects (seams) are implemented by face weights with special values of the spectral parameter. Integrability allows the study of lattice transfer matrix T- and Y-system functional equations to reproduce the fusion algebra of defect lines. The effective central charges and conformal weights are expressed in terms of dilogarithms of the braid and bulk asymptotics of the Y-system expressed in terms of the quantum dimensions.

hep-th↗

arXiv2024

Revisiting the symmetry-resolved entanglement for non-invertible symmetries in $1{+}1$d conformal field theories

Recently, a framework for computing the symmetry-resolved entanglement entropy for non-invertible symmetries in $1{+}1$d conformal field theories has been proposed by Saura-Bastida, Das, Sierra and Molina-Vilaplana [Phys. Rev. D109, 105026]. We revisit their theoretical setup, paying particular attention to possible contributions from the conformal boundary conditions imposed at the entangling surface -- a potential subtlety that was not addressed in the original proposal. We find that the presence of boundaries modifies the construction of projectors onto irreducible sectors, compared to what can be expected from a pure bulk approach. This is a direct consequence of the fusion algebra of non-invertible symmetries being different in the presence or absence of boundaries on which defects can end. We apply our formalism to the case of the Fibonacci category symmetry in the three-state Potts and tricritical Ising model and the Rep($S_3$) fusion category symmetry in the $SU(2)_4$ Wess-Zumino-Witten conformal field theory. We numerically corroborate our findings by simulating critical anyonic chains with these symmetries as a finite lattice substitute for the expected entanglement Hamiltonian. Our predictions for the symmetry-resolved entanglement for non-invertible symmetries seem to disagree with the recent work by Saura-Bastida et al.

hep-th↗