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

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

2011-11-15

arxiv.org/abs/1111.3634v2

Physics

Condensed Matter

Strongly Correlated Electrons

6 pages, 2 figures, minor mistakes corrected in formulas (1), (2) and (8)

Scientific paper

We devise a simple way to calculate the dimensions of symmetry sectors appearing in the Particle Entanglement Spectrum (PES) and Real Space Entanglement Spectrum (RSES) of multi-particle systems, directly from their real space wave functions. Our method starts by noting that the multiplicities in the entanglement spectra equal the dimensions of spaces of wave functions with a number of particles fixed. This also yields a simple argument that these multiplicities are the same for the PES and the RSES. Our technique allows us to numerically obtain results for much larger systems than were previously feasible. As a first application, we present a summary of results of our calculations for integer quantum Hall states, Laughlin states and the non-Abelian Moore-Read Pfaffian state at filling $\nu=5/2$.

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