Multivaluedness of the Luttinger-Ward functional in the fermionic and bosonic system with replicas

@article{Kim2020MultivaluednessOT,
  title={Multivaluedness of the Luttinger-Ward functional in the fermionic and bosonic system with replicas},
  author={Aaram J. Kim and V. E. Sacksteder},
  journal={Physical Review B},
  year={2020}
}
We study the properties of the Luttinger-Ward functional (LWF) in a simplified 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 fermionic statistics. We show that fermionic statistics are directly linked to the fact that multiple values of the noninteracting Green function $G_0$ map to the same value of the interacting Green… 

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