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Entanglement Resolution with Respect to Conformal Symmetry

Christian Northe

Abstract

Entanglement is resolved in conformal field theory (CFT) with respect to conformal families to all orders in the UV cutoff. To leading order, symmetry-resolved entanglement is connected to the quantum dimension of a conformal family, while to all orders it depends on null vectors. Criteria for equipartition between sectors are provided in both cases. This analysis exhausts all unitary conformal families. Furthermore, topological entanglement entropy is shown to symmetry-resolve the Affleck-Ludwig boundary entropy. Configuration and fluctuation entropy are analyzed on grounds of conformal symmetry.

Entanglement Resolution with Respect to Conformal Symmetry

Abstract

Entanglement is resolved in conformal field theory (CFT) with respect to conformal families to all orders in the UV cutoff. To leading order, symmetry-resolved entanglement is connected to the quantum dimension of a conformal family, while to all orders it depends on null vectors. Criteria for equipartition between sectors are provided in both cases. This analysis exhausts all unitary conformal families. Furthermore, topological entanglement entropy is shown to symmetry-resolve the Affleck-Ludwig boundary entropy. Configuration and fluctuation entropy are analyzed on grounds of conformal symmetry.
Paper Structure (7 sections, 53 equations, 1 figure)

This paper contains 7 sections, 53 equations, 1 figure.

Table of Contents

  1. Characters and null vectors
  2. Quantum dimensions
  3. Asymptotic entropy expansions
  4. Entropy Decompositions
  5. (Symmetry-resolved) Rényi entropies in terms of $S^{\mathsf{Verma}}_{1}$ and $s^{\alpha\beta}_1$
  6. Configuration and fluctuation entropy at all $n$ for complete equipartition
  7. Asymptotic equipartition in Virasoro minimal models

Figures (1)

  • Figure 1: The Factorization $\iota_{\alpha\beta}$ imposes disks with boundary conditions $\alpha,\beta$, thereby placing the system on the manifold $\mathcal{R}$. Replicating this to $\mathcal{R}_n$, tracing over $\mathcal{H}_{B,\alpha\beta}$ and a subsequent conformal transformation provides an annulus of width $W$ and circumference $2\pi n$.