Harmonic N-particle systems: reduced density operators and their properties

3 09/2014

Wednesday, 03 Sep. 2014, 10:00 - 11:30

Workgroup Verstraete Group

Presenter: Dr. Christian Schilling; Atomic & Laser Physics, University of Oxford
Host: Dr. James Whitfield
Where: Ernst-Mach-Hörsaal, 2nd Floor, Boltzmanngasse 5, 1090 Vienna

Solving analytically the N-particle Schrödinger equation for interacting particles is typically impossible. One exception is given by harmonic models which are also relevant from a physical viewpoint since they arise as an effective description of lattice systems. We present two results. First, we prove that for any eigenstate of a harmonic system each of its M-particle reduced density operators ρM obeys a duality condition. This condition implies duality relations for the eigenvalues λk of ρM and relates a harmonic model with length scales l1,….., lN with another one with inverse lengths 1/l1,….,1/lN. Entanglement entropies and correlation functions inherit duality from ρM. Second, for the specific case of N identical particles we explore the influence of the exchange statistics on the 1-particle properties obtained from ρ1. Although the (natural) occupation numbers for fermions and bosons differ significantly the fermionic and bosonic natural orbitals are very similar.