Reduced density matrix of permutational invariant many-body systems

TL;DR

This paper derives explicit formulas for the reduced density matrix of permutationally invariant many-body quantum systems, enabling analysis of their local properties and spectra.

Contribution

It provides a general analytic method to compute the reduced density matrix for blocks in permutational invariant systems, applicable when mean field theory is exact.

Findings

Explicit analytic expressions for RDM elements

Spectrum of RDM derived

Applicable to all permutational invariant systems with exact mean field

Abstract

We consider density matrices which are sums of projectors on states spanning irreducible representations of the permutation group of L sites (eigenstates of permutational invariant quantum system with L sites) and construct the reduced density matrix (RDM) for blocks of size n<L by tracing out L-n sites, viewed as environment. Explicit analytic expressions of the elements of the RDM are given in the natural basis and the corresponding spectrum is derived. Results apply to all quantum many-body systems with permutational symmetry for which the mean field theory is exact.