# 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…

## 4 Citations

Strange Metal Solution in the Diagrammatic Theory for the $2d$ Hubbard Model.

- Physics
- 2020

We show that the numerically exact bold-line diagrammatic theory for the $2d$ Hubbard model exhibits a non-Fermi-liquid (NFL) strange metal state, which is connected to the SYK NFL in the…

Tracking the Footprints of Spin Fluctuations: A MultiMethod, MultiMessenger Study of the Two-Dimensional Hubbard Model

- PhysicsPhysical Review X
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The Hubbard model represents the fundamental model for interacting quantum systems and electronic correlations. Using the two-dimensional half-filled Hubbard model at weak coupling as testing…

Physical and unphysical regimes of self-consistent many-body perturbation theory

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- 2021

In the standard framework of self-consistent many-body perturbation theory, the skeleton series for the self-energy is truncated at a finite order N and plugged into the Dyson equation, which is then…

Causal optimization method for imaginary-time Green's functions in interacting electron systems

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A causal optimization method is developed that ensures causality in numerical calculations of Green’s functions in interacting electron systems and finds that intermediate-frequency behaviors of Green's functions are determined solely by causality, and noncausal statistical errors are removed very efficiently.

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