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arXiv:cond-mat/0207210 · Annales Henri Poincaré

Low Temperature Analysis of Two-Dimensional Fermi Systems with Symmetric Fermi Surface

G. Benfatto, A. Giuliani, V. Mastropietro

Published Mar 1, 2003• 9 citations
arXivHTMLPDF
DOI
10.1007/s00023-003-0125-9

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We analyze the particle-hole symmetric two-dimensional Hubbard model on a square lattice starting from weak-to-moderate couplings by means of the field-theoretical renormalization group approach up to two-loop order. This method is essential in order to evaluate the effect of the momentum-resolved anomalous dimension $\ensuremath{\eta}(\mathbf{p})$ which arises in the normal phase of this model on the corresponding low-energy single-particle excitations. As a result, we find important indications pointing to the existence of a non-Fermi-liquid (NFL) regime at temperature $T\ensuremath{\rightarrow}0$ displaying a truncated Fermi surface (FS) for a doping range exactly in between the well-known antiferromagnetic insulating and the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave singlet superconducting phases. This NFL evolves as a function of doping into a correlated metal with a large FS before the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave pairing susceptibility finally produces the dominant instability in the low-energy limit.
At the low energy regime, the decay rate of two-dimensional massless Dirac fermions due to interactions can be written as ImΣ(ω)∝∣ω∣x\mathrm{Im}Σ(ω) \propto |ω|^{x}ImΣ(ω)∝∣ω∣x at zero temperature. We find that the fermion system has: I) no sharp Fermi surface and no well-defined quasiparticle peak for 010101. In the presence of long-range gauge/Coulomb interaction or certain massless boson mode, the system exhibits unusual behavior belonging to class II.