2023/03/23 by Wang, Zhituo
#FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Probability (math.PR)
paper · doi:10.48550/arxiv.2303.13628
We study the low temperature properties of the two-dimensional weakly interacting Hubbard model on \ZZZ2 with renormalized chemical potential μ=2-μ0, 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 ł in the domain ł∈\RRT=\ł∈\RRR,\vertλlog2(μ0T/C1)|≤ C2\ for any fixed temperature T>0, suggesting that there is a phase transition with critical temperature Tc= (C1)/(\m0)exp(-C1/22|λ|-1/2). Here C1, C2 are positive constants independent of T and ł. 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.