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We devise a way to calculate the dimensions of symmetry sectors appearing inthe Particle Entanglement Spectrum (PES) and Real Space Entanglement Spectrum(RSES) of multi-particle systems from their real space wave functions. We firstnote that these ranks in the entanglement spectra equal the dimensions ofspaces of wave functions with a number of particles fixed. This also yieldsequality of the multiplicities in the PES and the RSES. Our technique allowsnumerical calculations for much larger systems than were previously feasible.For somewhat smaller systems, we can find approximate entanglement energies aswell as multiplicities. We illustrate the method with results on the RSES andPES multiplicities for integer quantum Hall states, Laughlin and Jain compositefermion states and for the Moore-Read state at filling $\nu=5/2$, for systemsizes up to 70 particles.

Evaluation of ranks of real space and particle entanglement spectra for large systems