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 $(\pi /2,\pi /2)$ 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.

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

References in corpus (30)

• Quantum oscillations and the Fermi surface in an underdoped high-Tc superconductor
• Electron pockets in the Fermi surface of hole-doped high-Tc superconductors
• Distinct Fermi-Momentum Dependent Energy Gaps in Deeply Underdoped Bi2212
• A Phenomenological Theory of The Pseudogap State
• Two Energy Scales and two Quasiparticle Dynamics in the Superconducting State of Underdoped Cuprates
• A multi-component Fermi surface in the vortex state of an underdoped high-Tc superconductor
• Shubnikov-de Haas oscillations in YBa_2Cu_4O_8
• Coexistence of Fermi arcs and Fermi pockets in a high Tc copper oxide superconductor
• de Haas-van Alphen oscillations in the underdoped cuprate YBa${}_2$Cu${}_3$O${}_{6.5}$
• Modeling the Fermi arc in underdoped cuprates
• On the Reconstructed Fermi Surface in the Underdoped Cuprates
• Doped high-Tc cuprate superconductors elucidated in the light of zeros and poles of electronic Green's function
• Competition between spin density wave order and superconductivity in the underdoped cuprates
• Effective theory of Fermi pockets in fluctuating antiferromagnets
• Measurement of x-ray absorption spectra of overdoped high-temperature cuprate superconductors: Inapplicability of the single-band Hubbard model
• Cuprate Fermi orbits and Fermi arcs: the effect of short-range antiferromagnetic order
• Composite-Fermion Theory for Pseudogap, Fermi Arc, Hole Pocket, and Non-Fermi-Liquid of Underdoped Cuprate Superconductors
• Breakdown of Luttinger's theorem in two-orbital Mott insulators
• Breakup of the Fermi surface near the Mott transition in low-dimensional systems
• Mottness in High-Temperature Copper-Oxide Superconductors
• Structural origin of apparent Fermi surface pockets in angle-resolved photoemission of Bi${}_2$Sr${}_{2-x}$La${}_x$CuO${}_{6+\delta }$
• Hidden Charge 2e Boson in Doped Mott Insulators: Field Theory of Mottness
• Exact Integration of the High Energy Scale in Doped Mott Insulators
• Angle dependent quasiparticle weights in correlated metals
• Luttinger sum rule for finite systems of correlated electrons
• Hidden Charge 2e Boson: Experimental Consequences for Doped Mott Insulators
• Charge 2e Boson Underlies Two - Fluid Model of the Pseudogap in Cuprate Superconductors
• Violation of the Luttinger sum rule within the Hubbard model on a triangular lattice
• Influence of Thermal Fluctuations of Spin Density Wave Order Parameter on the Quasiparticle Spectral Function
• Non-conservation of Fermionic Degrees of Freedom at Low-energy in Doped Mott Insulators

Cited by in corpus (11)

• Un-Fermi Liquids: Unparticles in Strongly Correlated Electron Matter
• Pairing instability on a Luttinger surface: A non-Fermi liquid to superconductor transition and its Sachdev-Ye-Kitaev dual
• Superconductivity from Luttinger surfaces: Emergent $\infty$-body SYK physics
• Evolution of Holographic Fermi Arcs from a Mott Insulator
• Duality between zeroes and poles in holographic systems with massless fermions and a dipole coupling
• Linear-in-$T$ resistivity from semiholographic non-Fermi liquid models
• Probing the Holographic Fermi Arc with scalar field: Numerical and analytical study
• Studying the holographic Fermi surface in the scalar induced anisotropic background
• Non-equilibrium Transport in the Strange Metal and Pseudogap phases of the Cuprates
• Evolution of holographic Fermi surface from non-minimal couplings
• Characterizing Featureless Mott Insulating State by Quasiparticle Interferences - A Dynamical Mean Field Theory Prospect