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Honeycomb Hubbard Model at van Hove Filling

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Abstract

This paper is devoted to the rigorous study of the low temperature properties of the two-dimensional weakly interacting Hubbard model on the honeycomb lattice in which the renormalized chemical potential \(\mu \) has been fixed such that the Fermi surface consists of a set of exact triangles. Using renormalization group analysis around the Fermi surface, we prove that this model is not a Fermi liquid in the mathematically precise sense of Salmhofer. The main result is proved in two steps. First we prove that the perturbation series for Schwinger functions as well as the self-energy function have non-zero radius of convergence when the temperature T is above an exponentially small value, namely \({T_0\sim \exp {(-C|\lambda |^{-1/2})}}\). Then we prove the necessary lower bound for second derivatives of self-energy w.r.t. the external momentum and achieve the proof.

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Notes

  1. Although summation over all scales of the tadpole terms is not absolutely convergent for \(k_0\rightarrow \infty \), this sum can be controlled by using the explicit expression of the single scale propagator.

  2. The interested readers who are familiar with the sectors for strictly convex Fermi surfaces (cf. [6, 13, 14, 18]) are invited to compare the different decaying properties.

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Acknowledgements

Zhituo Wang is very grateful to Horst Knörrer for useful discussions and encouragements, and to Alessandro Giuliani and Vieri Mastropietro for useful discussions. Part of this work has been finished during Zhituo Wang’s visit to the Institute of Mathematics, University of Zurich. He is also very grateful to Benjamin Schlein for invitation and hospitality. We are grateful to the anonymous referee for his comments and suggestions, which lead to significant improvements of the first manuscript. Zhituo Wang is supported by NSFC Nos. 12071099 and 11701121. Vincent Rivasseau is supported by Paris-Saclay University and the IJCLab of the CNRS.

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  1. Laboratoire de Physique des 2 Infinis Irène Joliot-Curie, CNRS and Université Paris-Saclay, 91405, Orsay Cedex, France

    Vincent Rivasseau

  2. Institute for Advanced Study in Mathematics, Harbin Institute of Technology, Harbin, China

    Zhituo Wang

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  1. Vincent Rivasseau
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Correspondence to Zhituo Wang.

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Communicated by M. Salmhofer.

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Rivasseau, V., Wang, Z. Honeycomb Hubbard Model at van Hove Filling. Commun. Math. Phys. 401, 2569–2642 (2023). https://doi.org/10.1007/s00220-023-04696-8

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