Breakdown of the Fermi-liquid regime in the two-dimensional Hubbard model from a two-loop field-theoretical renormalization group approach

Abstract

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 ͑p͒ 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 ͑NFL͒ regime at temperature T → 0 displaying a truncated Fermi surface ͑FS͒ for a doping range exactly in between the well-known antiferromagnetic insulating and the d x 2 −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 −y 2-wave pairing susceptibility finally produces the dominant instability in the low-energy limit.͑p͒ contribution to the single-particle excitations, which arises only at a two-loop RG level or beyond close to half-PHYSICAL REVIEW B 78, 125114 ͑2008͒

Variational study of Fermi surface deformations in Hubbard models

“…For small U , the self-energy Σ(k, ω) may be calculated from straightforward perturbation theory [2][3][4], or using renormalization group methods [5,6]. When U is of the order of the bare bandwidth W , or larger, only purely numerical methods such as quantum monte Carlo [7,8] and exact diagonalisation [9] are available which still suffer from serious finite-size limitations [9,10].…”

Complete renormalization group calculation up to two-loop order of an effective two-band model for iron-based superconductors

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