The structure of fermion density matrices. III. Long-range order

Alan Coleman

Pirmin Lemberger, Nicolas Macris

Louis Witten

Chen Ning Yang

This review is concerned with the concept that in a many-body system of bosons or fermions, it is possible to have an off-diagonai long-range order of the reduced density matrices in the coordinate space representation. The onset of such an order ieads to a new thermodynamic phase of the system. It is reasonabie to assume that superfluid He II and the superconductors are phases characterized by the existence of such an order. (W.D.M.)

Akiko Masaki, Sota Tsukada, 弘之 森

We numerically studied internal structure of Mott insulating state of Bose–Fermi mixture systems on a one-dimensional optical lattice by using quantum Monte Carlo simulations. We looked for Mott state carefully adjusting various parameters to prevent phase separation. From the calculation of density–density correlation functions we found a quasi long-range order in the particle distribution in the Mott state. The order was strongly dependent of the ratio of the number of the bosons to that of the fermions. For example, the bosons and the fermions showed a tendency of aligning alternately when equal number of the bosons and fermions are introduced in the system. The observation of the quasi long-range order in the one-dimensional system indicates the presence of true long-range order in Bose–Fermi mixtures on a three-dimensional optical lattice.

Donald Wright

The thermodynamic properties of the hard-sphere Bose gas are calculated from the one- and two-particle density matrices. The one- and two-particle density matrices are evaluated in the Bogoliubov approximation. The off-diagonal elements of the one- and two-particle density matrices are studied for the presence or absence of off-diagonal long-range order in various temperature regions. Off-diagonal long-range order was found in the single-particle density matrix below the Bose-Einstein transition temperature. The two-particle density matrix also exhibited off-diagonal long-range order whenever the single-particle density matrix did.