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arXiv:1907.12553

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

Zhituo Wang

Published Jul 29, 2019• 0 citations
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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 $μ$, which is fixed to be $1$. We prove that the two-point Schwinger's function is an analytic function of the coupling constant $λ$ in the domain $|λ|\cdot|\log T|^2<1$. 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.

DOI
10.48550/arxiv.1907.12553

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We study the low temperature properties of the two-dimensional weakly interacting Hubbard model on $\ZZZ^2$ with renormalized chemical potential μ=2−μ0μ=2-μ_0μ=2−μ0​, μ0=10−10μ_0=10^{-10}μ0​=10−10 fixed, in which case the Fermi surface is close to a perfect square. Using fermionic functional integrals, cluster expansions and rigorous renormalization group analysis, we prove that the perturbation series for the two-point Schwinger function is analytic in the coupling constant łłł in the domain $ł\in\RR_T=\{ł\in\RRR,\vertλ\log^2(μ_0T/C_1)|\le C_2\}$ for any fixed temperature T>0T>0T>0, suggesting that there is a phase transition with critical temperature $T_c= \frac{C_1}{\m_0}\exp{(-C^{1/2}_2|λ|^{-1/2})}$. Here C1,C2C_1, C_2C1​,C2​ are positive constants independent of TTT and łłł. We also prove that the second derivative of the momentum space self-energy function w.r.t. the external momentum is not uniformly bounded, suggesting that this model is {\it not} a Fermi liquid in the mathematically precise sense of Salmhofer. This result can be viewed as a first step towards rigorous study of the Fermi liquid-non Fermi liquid crossover phenomenon.
In this paper we complete the proof that the honeycomb Hubbard model with renormalized chemical potential μ=1μ=1μ=1 is {\it not} a Fermi liquid in the mathematically precise sense of Salmhofer, by establishing the necessary lower bounds for second derivatives of the self-energy w.r.t. the external momentum.
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Abstract. We prove that the weak coupling 2D Hubbard model away from half filling is a Landau Fermi liquid up to exponentially small temperatures. In particular we show that the wave function renormalization is an order 1 constant and essentially temperature independent in the considered range of temperatures and that the interacting Fermi surface is a regular convex curve. This result is obtained by deriving a convergent expansion (which is not a power series) for the two point Schwinger function by Renormalization Group methods and proving at each order suitable power counting improvements due to the convexity of the interacting Fermi surface. Convergence follows from determinant bounds for the fermionic expectations.
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