On Calculating Approximate and Exact Density Matrices

George Starkschall, John C. Light

Using an analytic approximation to the quantum momentum previously derived to calculate single particle reduced density matrices in the semiclassical approximation, we have been able to construct equations of motion with which to perform trajectory calculations. Information calculated along these trajectories is used to calculate single particle reduced density matrices for one-dimensional systems. Charge densities for N fermions in a harmonic oscillator potential calculated using this quantum momentum approximation are in excellent agreement with the exact quantum mechanical calculations.

K. Husimi, Yoshihiro Kitano, Toshiyuki Nishiyama

Karl Blum

Omar Osenda, Federico M. Pont, Anna Okopińska +1 more

The information content of continuous quantum variables systems is usually studied using a number of well known approximation methods. The approximations are made to obtain the spectrum, eigenfunctions or the reduced density matrices that are essential to calculate the entropy-like quantities that quantify the information. Even in the sparse cases where the spectrum and eigenfunctions are exactly known the entanglement spectrum, {\em i.e.} the spectrum of the reduced density matrices that characterize the problem, must be obtained in an approximate fashion. In this work, we obtain analytically a finite representation of the reduced density matrices of the fundamental state of the N-particle Calogero model for a discrete set of values of the interaction parameter. As a consequence, the exact entanglement spectrum and von Neumann entropy is worked out.

Bernd Esser

Jack Simons, John E. Harriman

A method is given for obtaining the density matrix or matrices, expressible in terms of a given set of spin geminals, which are as nearly $N$ representable as possible. A measure of $N$ representability is introduced as the norm of the antisymmetric component of a normalized wave function leading to the density matrix. An error estimate is given for the maximum deviation of an energy calculated with the density matrix from that calculated with an antisymmetric wave function. Linear variational parameters may occur in the density matrix, and their number can be increased at the expense of $N$ representability. Implementation of the method requires diagonalization of a large matrix, and the consequences of truncation are considered. The method is also related to the problem of the exact $N$ representability of a given density matrix.