Noninvertible Symmetry-Resolved Affleck-Ludwig-Cardy Formula and Entanglement Entropy from the Boundary Tube Algebra

Area of Science:

• Theoretical Physics
• Quantum Field Theory
• Condensed Matter Physics

Background:

• The Affleck-Ludwig-Cardy formula describes state densities in conformal field theories.
• Noninvertible global symmetries introduce new complexities in quantum systems.
• Entanglement entropy quantifies quantum correlations in subsystems.

Purpose of the Study:

• To derive a refined Affleck-Ludwig-Cardy formula for 1+1D conformal field theories with noninvertible symmetries.
• To compute universal contributions to noninvertible symmetry-resolved entanglement entropy.
• To investigate the symmetry properties of the double Ising model's entanglement Hamiltonian.

Main Methods:

• Derivation of a refined Affleck-Ludwig-Cardy formula.
• Analysis of noninvertible symmetry-resolved entanglement entropy.
• Application to the critical double Ising model with specific boundary conditions.
• Utilizing recent advancements in symmetry topological field theories.

Main Results:

• A refined formula for asymptotic density of high energy states under noninvertible symmetries.
• Determination of universal leading and subleading contributions to symmetry-resolved entanglement entropy.
• Identification of a Kac-Paljutkin H8 Hopf algebra symmetry in the double Ising model's ground state entanglement Hamiltonian.
• Calculation of corresponding symmetry-resolved entanglement entropies for the double Ising model.

Conclusions:

• The refined formula provides a powerful tool for studying quantum systems with noninvertible symmetries.
• The findings offer new insights into the structure of entanglement and symmetry in critical phenomena.
• The concrete example of the double Ising model demonstrates the practical application of the derived methods.