# 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}

}