Kavli Affiliate: Hirosi Ooguri
| First 5 Authors: Yuya Kusuki, Sara Murciano, Hirosi Ooguri, Sridip Pal,
| Summary:
We perform a comprehensive analysis of the symmetry-resolved (SR)
entanglement entropy (EE) for one single interval in the ground state of a
$1+1$D conformal field theory (CFT), that is invariant under an arbitrary
finite or compact Lie group, $G$. We utilize the boundary CFT approach to study
the total EE, which enables us to find the universal leading order behavior of
the SREE and its first correction, which explicitly depends on the irreducible
representation under consideration and breaks the equipartition of
entanglement. We present two distinct schemes to carry out these computations.
The first relies on the evaluation of the charged moments of the reduced
density matrix. This involves studying the action of the defect-line, that
generates the symmetry, on the boundary states of the theory. This perspective
also paves the way for discussing the infeasibility of studying symmetry
resolution when an anomalous symmetry is present. The second scheme draws a
parallel between the SREE and the partition function of an orbifold CFT. This
approach allows for the direct computation of the SREE without the need to use
charged moments. From this standpoint, the infeasibility of defining the
symmetry-resolved EE for an anomalous symmetry arises from the obstruction to
gauging. Finally, we derive the symmetry-resolved entanglement spectra for a
CFT invariant under a finite symmetry group. We revisit a similar problem for
CFT with compact Lie group, explicitly deriving an improved formula for $U(1)$
resolved entanglement spectra. Using the Tauberian formalism, we can estimate
the aforementioned EE spectra rigorously by proving an optimal lower and upper
bound on the same. In the abelian case, we perform numerical checks on the
bound and find perfect agreement.
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