Total and Symmetry resolved Entanglement spectra in some Fermionic CFTs from the BCFT approach

• Main Author: Gaur, Himanshu
• Format: Journal Article
• Language: English
• Published: 23-09-2024
• Subjects: Physics - High Energy Physics - Theory; Physics - Quantum Physics
• DOI: 10.48550/arxiv.2402.07557

JHEP09(2024)173 In this work, we study the universal total and symmetry-resolved entanglement
spectra for a single interval of some $2$d Fermionic CFTs using the Boundary
Conformal Field theory (BCFT) approach. In this approach, the partition of
Hilbert space is achieved by cutting out discs around the entangling boundary
points and imposing boundary conditions preserving the extended symmetry under
scrutiny. The reduced density moments are then related to the BCFT partition
functions and are also found to be diagonal in the symmetry charge sectors. In
particular, we first study the entanglement spectra of massless Dirac fermion
and modular invariant $Z_2$-gauged Dirac fermion by considering the boundary
conditions preserving either the axial or the vector $U(1)$ symmetry. The total
entanglement spectra of the modular invariant Dirac fermion are shown to match
with the compact boson result at the Bose-Fermi duality radius, while for the
massless Dirac fermion, it is found that the boundary entropy term doesn't
match with the self-dual compact boson. The symmetry-resolved entanglement is
found to be the same in all cases, except for the charge spectrum which is
dependent on both the symmetry and the theory. We also study the entanglement
spectra of $N$ massless Dirac fermions by considering boundary conditions
preserving different chiral $U(1)^N$ symmetries. Entanglement spectra are
studied for $U(1)^M$ subgroups, where $M\leq N$, by imposing boundary
conditions preserving different chiral symmetries. The total entanglement
spectra are found to be sensitive to the representations of the $U(1)^M$
symmetry in the boundary theory among other behaviours at $O(1)$. Similar
results are also found for the Symmetry resolved entanglement entropies. The
characteristic $\log\log\left(\ell/\epsilon\right)$ term of the $U(1)$ symmetry
is found to be proportional to $M$ in the symmetry-resolved entanglement
spectra.