Stabilizer Rényi Entropy Encodes Fusion Rules of Topological Defects and Boundaries.

Area of Science:

• Condensed Matter Physics
• Quantum Information Theory
• High Energy Physics

Background:

• Quantum critical systems exhibit universal behavior governed by conformal field theories.
• Conformal defects introduce topological order and non-invertible symmetries.
• Stabilizer Rényi entropy (SRE) is a computable measure of quantum magic.

Purpose of the Study:

• To utilize SRE as an information-theoretic tool to probe universal properties of conformal defects in 1D quantum critical systems.
• To establish a connection between SRE, boundary/defect properties, and non-invertible symmetry algebras.

Main Methods:

• Analytical calculations using boundary conformal field theory (BCFT).
• Investigating the behavior of SRE in the presence of open boundaries and topological defects.
• Numerical simulations of the Ising model to corroborate analytical predictions.

Main Results:

• Open boundaries introduce a universal logarithmic correction to the SRE.
• Topological defects contribute a universal, size-independent term to the SRE.
• The SRE's universal terms accurately reflect defect-fusion rules defining non-invertible symmetries.

Conclusions:

• SRE serves as a powerful information-theoretic probe for universal properties of conformal defects.
• The study provides a framework for understanding non-invertible symmetries via SRE in quantum critical systems.
• Analytical and numerical results confirm the utility of SRE in characterizing topological defects and boundaries.