skip to main content

Title: Particle–hole ring diagrams for fermions in two dimensions

The set of particle–hole ring diagrams for a many-fermion system in two dimensions is studied. The complex-valued polarization function is derived in detail and shown to be expressible in terms of square-root functions. For a contact-interaction the perturbative contributions to the energy per particle Ē(k{sub f}) are calculated in a closed analytical form from third up to twelfth order. The resummation of the particle–hole ring diagrams to all orders is studied and a pronounced dependence on the dimensionless coupling parameter α is found. There is a substantial difference between the complete ring-sum with all exchange-type diagrams included and the standard resummation of the leading n-ring diagrams only. The spin factor S{sub n}(g) associated to the nth order ring diagrams is derived for arbitrary spin-degeneracy g.
Authors:
Publication Date:
OSTI Identifier:
22403450
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics (New York); Journal Volume: 350; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DIAGRAMS; FERMIONS; FUNCTIONS; HOLES; MANY-BODY PROBLEM; PARTICLES; POLARIZATION; RINGS; SPIN; TWO-DIMENSIONAL CALCULATIONS; TWO-DIMENSIONAL SYSTEMS