Functional renormalization group for non-Hermitian and $\mathcal{PT}$-symmetric systems

Grunwald, Lukas; Meden, Volker; Kennes, Dante M.

doi:10.21468/SciPostPhys.12.5.179

SciPost Physics

Functional renormalization group for non-Hermitian and $\mathcal{PT}$-symmetric systems

Lukas Grunwald, Volker Meden, Dante M. Kennes

SciPost Phys. 12, 179 (2022) · published 30 May 2022

doi: 10.21468/SciPostPhys.12.5.179
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Abstract

We generalize the vertex expansion approach of the functional renormalization group to non-Hermitian systems. As certain anomalous expectation values might not vanish, additional terms as compared to the Hermitian case can appear in the flow equations. We investigate the merits and shortcomings of the vertex expansion for non-Hermitian systems by considering an exactly solvable $\mathcal{PT}$-symmetric non-linear toy-model and reveal, that in this model, the fidelity of the vertex expansion in a perturbatively motivated truncation schema is comparable with that of the Hermitian case. The vertex expansion appears to be a viable method for studying correlation effects in non-Hermitian systems.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.12.5.179
TI  - Functional renormalization group for non-Hermitian and $\mathcal{PT}$-symmetric systems
PY  - 2022/05/30
UR  - https://www.scipost.org/SciPostPhys.12.5.179
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 12
IS  - 5
SP  - 179
A1  - Grunwald, Lukas
AU  - Meden, Volker
AU  - Kennes, Dante M.
AB  - We generalize the vertex expansion approach of the functional renormalization group to non-Hermitian systems. As certain anomalous expectation values might not vanish, additional terms as compared to the Hermitian case can appear in the flow equations. We investigate the merits and shortcomings of the vertex expansion for non-Hermitian systems by considering an exactly solvable $\mathcal{PT}$-symmetric non-linear toy-model and reveal, that in this model, the fidelity of the vertex expansion in a perturbatively motivated truncation schema is comparable with that of the Hermitian case. The vertex expansion appears to be a viable method for studying correlation effects in non-Hermitian systems.
ER  -

@Article{10.21468/SciPostPhys.12.5.179,
	title={{Functional renormalization group for non-Hermitian and $\mathcal{PT}$-symmetric systems}},
	author={Lukas Grunwald and Volker Meden and Dante M. Kennes},
	journal={SciPost Phys.},
	volume={12},
	pages={179},
	year={2022},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.12.5.179},
	url={https://scipost.org/10.21468/SciPostPhys.12.5.179},
}

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