English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We study the properties of the Luttinger-Ward functional (LWF) in asimplified Hubbard-type model without time or spatial dimensions, but with $N$identical replicas located on a single site. The simplicity of this $(0+0)d$model permits an exact solution for all $N$ and for both bosonic and fermionicstatistics. We show that fermionic statistics are directly linked to the factthat multiple values of the noninteracting Green function $G_0$ map to the samevalue of the interacting Green function $G$, i.e. the mapping $G_0 \mapsto G$is non-injective. This implies that with fermionic statistics the $(0+0)d$model has a multiply-valued LWF. The number of LWF values in the fermionicmodel increases proportionally to the number of replicas $N$, while in thebosonic model the LWF has a single value regardless of $N$. We also discuss theformal connection between the $(0+0)d$ model and the $(0+1)d$ model which wasused in previous studies of LWF multivaluedness.

Multi-valuedness of the Luttinger-Ward functional in the Fermionic and Bosonic System with Replicas