# Non-Fermi Liquid Behaviors in the Hubbard model on the Honeycomb lattice

## TL;DR

This paper investigates the low-temperature behaviors of the weakly interacting Hubbard model on a honeycomb lattice, revealing non-Fermi liquid properties through analytic and ground state analysis.

## Contribution

It provides a rigorous proof that the Hubbard model exhibits non-Fermi liquid behavior at low temperatures on the honeycomb lattice.

## Key findings

- Two-point Schwinger's function is analytic in the coupling constant.
- Ground state does not satisfy Fermi liquid criteria.
- Model exhibits non-Fermi liquid behavior at low temperatures.

## Abstract

In this paper we study the low temperature ($T\rightarrow 0$) behaviors of the weakly interacting Hubbard model on the honeycomb lattice with a bare chemical potential, which takes values in a small neighborhood of the renormalized chemical potential $\mu$, which is fixed to be $1$. We prove that the two-point Schwinger's function is an analytic function of the coupling constant $\lambda$ in the domain $|\lambda|\cdot|\log T|^2<1$. But the ground state of this model is not a Fermi liquid, because analytic properties of self-energy don't satisfy the Salmhofer's criterion on the Fermi liquids at finite temperature.