On Hugenholtz-Pines' Theory about Ground State Energy of Interacting Bosons

Emilio Borchi, M. Poli

Abdulla Rakhimov, Asliddin Khudoyberdiev

節夫 三沢

Hugenholtz and Pines have developed a new method evaluate the ground state energy of a system of interacting bosons, the merit of which consists in the elimination of ' the zero-momentam state and accordingly the applicability of the linked cluster expansion. Their theory, however, does not give correct results because of the undue treatment of the zero-momentum state; this is proved in a simple example. Up to the third order coupling parameter of the ground state enengy, the result of the usual RayleighSchrodinger perturbation method are compared with that obtained according to Hugenholtz-Pines' theory. The latter does not agree with the former. (auth)

Peter A. Ring, Y. K. Gambhir, S. Iwasaki +1 more

Colin John Lambert

We examine in detail the microscopic theories of Beliaev and Hugenholtz and Pines as applied to an interacting system of bosons in its ground state and demonstrate that these theories are strictly applicable to a zero density gas only. After providing a re-normalization of the time dependent perturbation theory of a many fermion system in its ground state, we reformulate the corresponding boson theory without ab initio approximations concerning the k=0 mode.The resulting boson perturbation theory has a diagrammatic structure which is topologically identical with the corresponding fermion theory and provided the implicit assumptions concerning convergence are valid, we conclude that a finite fraction of the particles in an arbitrary interacting Bose gas at T=ok will not condense into the k=0 mode.

M. L. Chiofalo, Sergio Conti, Monica Tosi

We derive and discuss sets of sum rules relating to the density fluctuation operator and to the single-particle creation and annihilation operators in a superfluid of charged bosons. The physical interpretation of the particle - particle and particle - density sum rules hinges on the single-particle excitation spectrum at long wavelengths having a gap equal to the plasma frequency in the presence of the Bose - Einstein condensate. This spectral property is shown to follow from the Hugenholtz - Pines relation for the chemical potential in terms of the half-diagonal two-body density matrix. Data on this density matrix are obtained by quantum Monte Carlo methods and are used to check the self-consistency between the Hugenholtz - Pines relation and the value of the chemical potential calculated from the ground-state energy. We also tabulate the contributions from the plasmon and from multiparticle excitations to various matrix elements and sum rules at long wavelengths.