Breakdown of the Fermi-liquid regime in the 2D 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 (RG) approach up to two-loop order. This method is essential in order to evaluate the effect of the momentum-resolved anomalous dimension $\eta (\text{p})$ 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 $T\to 0$ displaying a truncated Fermi surface (FS) 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.

9 pages, 9 figures; published in Phys. Rev. B

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• Extended quantum criticality of low-dimensional superconductors near a spin-density-wave instability
• Evidence of a short-range incommensurate $d$-wave charge order from a fermionic two-loop renormalization group calculation of a 2D model with hot spots
• Accessing the ordered phase of correlated Fermi systems: vertex bosonization and mean-field theory within the functional renormalization group
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