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

TL;DR

This paper derives a theoretical model from the Hubbard model that explains Fermi arcs and pseudogap phenomena in cuprate superconductors through emergent charge excitations and spectral features.

Contribution

It introduces a Wilsonian reduction of the Hubbard model revealing composite excitations responsible for Fermi arcs and pseudogaps in cuprates.

Findings

Fermi arcs arise from poles in the Green function at specific momenta.

Zeros in the Green function suppress spectral weight, shaping the arc.

Composite excitations explain the pseudogap and nodal/anti-nodal dichotomy.

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 $(\pi/2,\pi/2)$ 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 $(\pi,0)$ region of the Brillouin zone, thereby providing a mechanism for the nodal/anti-nodal dichotomy seen in the cuprates.