Reduced density matrices with nonzero boundary conditions in the case of a hard core

К. С. Матвийчук

К. С. Матвийчук

J. Ginibre

In two previous papers, the reduced density matrices of quantum gases, in the grand canonical formalism and for suitably restricted interaction potentials, have been shown to be analytic vector-valued functions of the activity in a neighborhood of the origin, to tend in some sense to well-defined limits as the volume of the system becomes infinite, and to satisfy a cluster decomposition property. The same results are extended here by the same methods to a wider class of potentials, including hard-core, and allowing attractive interactions, which were excluded previously.

Eugene S. Kryachko

Michael Assis, Jesper Lykke Jacobsen, Iwan Jensen +2 more

In this paper we compare the integrable hard hexagon model with the non-integrable hard squares model by means of partition function roots and transfer matrix eigenvalues. We consider partition functions for toroidal, cylindrical, and free–free boundary conditions up to sizes 40 × 40 and transfer matrices up to 30 sites. For all boundary conditions the hard squares roots are seen to lie in a bounded area of the complex fugacity plane along with the universal hard core line segment on the negative real fugacity axis. The density of roots on this line segment matches the derivative of the phase difference between the eigenvalues of largest (and equal) moduli and exhibits much greater structure than the corresponding density of hard hexagons. We also study the special point of hard squares, where all eigenvalues have unit modulus, and we give several conjectures for the value at of the partition functions.