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We investigate the effect of a global degeneracy in the distribution ofentanglement spectrum in conformal field theories in one spatial dimension. Werelate the recently found universal expression for the entanglement hamiltonianto the distribution of the entanglement spectrum. The main tool to establishthis connection is the Cardy formula. It turns out that the Affleck-Ludwignon-integer degeneracy, appearing because of the boundary conditions induced atthe entangling surface, can be directly read from the entanglement spectrumdistribution. We also clarify the effect of the non-integer degeneracy on thespectrum of the partial transpose, which is the central object for quantifyingthe entanglement in mixed states. We show that the exact knowledge of theentanglement spectrum in some integrable spin-chains provides strong analyticalevidences corroborating our results.

Entanglement spectrum degeneracy and Cardy formula in 1+1 dimensional conformal field theories