Real space entanglement spectra

I will present a way to calculate the Particle Entanglement Spectrum (PES) and Real Space Entanglement Spectrum (RSES) of multi-particle systems from their real space wave functions. The ranks of symmetry sectors in these entanglement spectra are shown to equal the dimensions of spaces of wave functions with a number of particles fixed, which yields equality of these ranks in the PES and the RSES. Our technique allows numerical calculations of ranks for much larger systems than were previously feasible. For somewhat smaller systems, we can find entanglement energies as well as multiplicities. The method is illustrated with results on the RSES and PES multiplicities for various families of fractional quantum Hall states, including Laughln, Moore-Read and Jain composite fermion states