skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

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

Abstract

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

Citation Formats

Kaiser, N., E-mail: nkaiser@ph.tum.de. Particle–hole ring diagrams for fermions in two dimensions. United States: N. p., 2014. Web. doi:10.1016/J.AOP.2014.07.045.
Kaiser, N., E-mail: nkaiser@ph.tum.de. Particle–hole ring diagrams for fermions in two dimensions. United States. doi:10.1016/J.AOP.2014.07.045.
Kaiser, N., E-mail: nkaiser@ph.tum.de. Sat . "Particle–hole ring diagrams for fermions in two dimensions". United States. doi:10.1016/J.AOP.2014.07.045.
@article{osti_22403450,
title = {Particle–hole ring diagrams for fermions in two dimensions},
author = {Kaiser, N., E-mail: nkaiser@ph.tum.de},
abstractNote = {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.},
doi = {10.1016/J.AOP.2014.07.045},
journal = {Annals of Physics (New York)},
number = ,
volume = 350,
place = {United States},
year = {Sat Nov 15 00:00:00 EST 2014},
month = {Sat Nov 15 00:00:00 EST 2014}
}