Breakdown of the Landau-Fermi liquid in two dimensions due to umklapp scattering - art. no. 035109

We study the renormalization-group (RG) flow of interactions in the two-dim ensional t-t' Hubbard model near half-filling in an N-patch representation of the whole Fermi surface. Starting from weak to intermediate couplings th e flows are to strong coupling, with different characters depending on the choice of parameters. In a large parameter region elastic umklapp scatterin gs drive an instability which on parts of the Fermi surface exhibits the ke y signatures of an insulating spin liquid (ISL), as proposed by Furukawa, R ice, and Salmhofer [Phys. Rev. Lett. 81, 3195 (1998)] rather than a convent ional symmetry-broken state. The ISL is characterized by both strong d-wave pairing and antiferromagnetic correlations; however, it is insulating due to the vanishing local charge compressibility and a spin liquid because of the spin gap arising from the pairing correlations. We find that the unusua l RG flow, which we interpret in terms of an ISL, is a consequence of a Fer mi surface close to the saddle points at the Brillouin-zone boundaries whic h provides an intrinsic and mutually reinforcing coupling between pairing a nd umklapp channels.