Towards the Standard Model of Fermi Arcs from a Wilsonian Reduction of the Hubbard Model

Abstract

Two remarkable features emerge from the exact Wilsonian procedure for integrating out the high-energy scale in the Hubbard model. At low energies, the number of excitations that couple minimally to the electromagnetic gauge is less than the conserved charge, thereby implying a breakdown of Fermi liquid theory. In addition, two charge $e$ excitations emerge in the lower band, the standard projected electron and a composite entity (comprised of a hole and a charge $2e$ bosonic field) which give rise to poles and zeros of the single-particle Green function, respectively. The poles generate spectral weight along an arc centered at $(π/2,π/2)$ while the zeros kill the spectral intensity on the back-side of the arc. The result is the Fermi arc structure intrinsic to cuprate phenomenology. The presence of composite excitations also produces a broad incoherent pseudogap feature at the $(π,0)$ region of the Brillouin zone, thereby providing a mechanism for the nodal/anti-nodal dichotomy seen in the cuprates.

8 pages, 4 figures: Extended version accepted to PRB. Additions include: 1) proof that the (π,π) solution is a global minimum, 2) extensive discussion of relation to SU(2) gauge theory of t-J model and 3) the meaning of the zero modes given the absence of Luttinger's theorem established in arXiv:1207.4201. New Published version