We prove analyticity theorems in the coupling constant for the Hubbard model at half-filling. The model in a single renormalization group slice of index $i$ is proved to be analytic in $λ$ for $|λ| \le c/i$ for some constant $c$ , and the skeleton part of the model at temperature $T$ (the sum of all graphs without two point insertions) is proved to be analytic in $λ$ for $|λ| \le c/|\log T|^{2}$ . These theorems are necessary steps towards proving that the Hubbard model at half-filling is {\it not} a Fermi liquid (in the mathematically precise sense of Salmhofer).We prove analyticity theorems in the coupling constant for the Hubbard model at half-filling. The model in a single renormalization group slice of index $i$ is proved to be analytic in $λ$ for $|λ| \le c/i$ for some constant $c$, and the skeleton part of the model at temperature $T$ (the sum of all graphs without two point insertions) is proved to be analytic in $λ$ for $|λ| \le c/|\log T|^{2}$. These theorems are necessary steps towards proving that the Hubbard model at half-filling is {\it not} a Fermi liquid (in the mathematically precise sense of Salmhofer).

arXiv:cond-mat/0107118Jul 5, 20014 citations

The Two Dimensional Hubbard Model at Half-Filling. I. Convergent Contributions

Vincent Rivasseau

Journal of Statistical PhysicsFeb 1, 200217 citations

Functional Renormalization Group Analysis of the Half-Filled One-Dimensional Extended Hubbard Model

Ka-Ming Tam, Shan-Wen Tsai, David K Campbell

We study the phase diagram of the half-filled one-dimensional extended Hubbard model at weak coupling using a novel functional renormalization group (FRG) approach. The FRG method includes in a systematic manner the effects of the scattering processes involving electrons away from the Fermi points. Our results confirm the existence of a finite region of bond charge density wave, also known as a "bond order wave" near U=2V and clarify why earlier g-ology calculations have not found this phase. We argue that this is an example in which formally irrelevant corrections change the topology of the phase diagram. Whenever marginal terms lead to an accidental symmetry, this generalized FRG method may be crucial to characterize the phase diagram accurately.We study the phase diagram of the half-filled one-dimensional extended Hubbard model at weak coupling using a novel functional renormalization group (FRG) approach. The FRG method includes in a systematic manner the effects of the scattering processes involving electrons away from the Fermi points. Our results confirm the existence of a finite region of bond charge density wave, also known as a "bond order wave" near U=2V and clarify why earlier g-ology calculations have not found this phase. We argue that this is an example in which formally irrelevant corrections change the topology of the phase diagram. Whenever marginal terms lead to an accidental symmetry, this generalized FRG method may be crucial to characterize the phase diagram accurately.

arXiv:cond-mat/0505396Physical Review LettersJan 27, 200664 citations

We prove analyticity theorems in the coupling constant for the Hubbard model at half-filling. The model in a single renormalization group slice of index

i

is proved to be analytic in

λ

for

|λ| \le c/i

for some constant

c

, and the skeleton part of the model at temperature

T

(the sum of all graphs without two point insertions) is proved to be analytic in

λ

for

|λ| \le c/|\log T|^{2}

. These theorems are necessary steps towards proving that the Hubbard model at half-filling is {\it not} a Fermi liquid (in the mathematically precise sense of Salmhofer).