Expansion of the Gibbs potential for quantum many-body systems: general formalism with applications to the spin glass and the weakly nonideal Bose gas.
For general quantum systems the power expansion of the Gibbs potential and consequently the power expansion of the self-energy is derived in terms of the interaction strength. Employing a generalization of the projector technique, a compact representation of the general terms of the expansion results. The general aspects of the approach are discussed with special emphasis on the effects characteristic for quantum systems. The expansion is systematic and leads directly to contributions beyond the mean field of all thermodynamic quantities. These features are explicitly demonstrated and illustrated for two nontrivial systems, the infinite-range quantum spin glass and the weakly interacting Bose gas. The Onsager terms of both systems are calculated, which represent the first beyond-mean-field contributions. For the spin glass Thouless-Anderson-Palmer-like equations are presented and discussed in the paramagnetic region. The investigation of the Bose gas leads to a beyond-mean-field thermodynamic description. At the Bose-Einstein condensation temperature complete agreement is found with the results presented recently by alternative techniques.
Plefka
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Department of Solid State Physics, TU Darmstadt, D 64289 Darmstadt, Germany. timm@fkp.tu-darmstadt.de