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

TL;DR

This paper introduces a method to compute the dimensions of symmetry sectors in entanglement spectra of large multi-particle systems, enabling analysis of bigger systems and providing insights into their quantum states.

Contribution

The authors develop a technique to calculate symmetry sector dimensions in PES and RSES from wave functions, allowing analysis of larger systems than before.

Findings

Calculated entanglement spectrum multiplicities for systems up to 70 particles.

Demonstrated the method on various quantum Hall states, including Laughlin, Jain, and Moore-Read.

Established the equality of multiplicities in PES and RSES for these systems.

Abstract

We devise a 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 from their real space wave functions. We first note that these ranks in the entanglement spectra equal the dimensions of spaces of wave functions with a number of particles fixed. This also yields equality of the multiplicities in the PES and the RSES. Our technique allows numerical calculations for much larger systems than were previously feasible. For somewhat smaller systems, we can find approximate entanglement energies as well as multiplicities. We illustrate the method with results on the RSES and PES multiplicities for integer quantum Hall states, Laughlin and Jain composite fermion states and for the Moore-Read state at filling $\nu=5/2$, for system sizes up to 70 particles.