Un-Fermi Liquids: Unparticles in Strongly Correlated Electron Matter

Abstract

Since any non-trivial infrared dynamics in strongly correlated electron matter must be controlled by a critical fixed point, we argue that the form of the single-particle propagator can be deduced simply by imposing scale invariance. As a consequence, the unparticle picture proposed by Georgi\cite{georgi} is the natural candidate to describe such dynamics. Unparticle stuff is scale-invariant matter with no particular mass. Scale invariance dictates that the propagator has an algebraic form which can admit zeros and hence is a candidate to explain the ubiquitous pseudogap state of the cuprates. The non-perturbative electronic state formed out of unparticles we refer to as an un-Fermi liquid. We show that the underlying action of the continuous mass formulation of unparticles can be recast exactly as an action in anti de Sitter space. We find that this mapping fixes the scaling dimension of the unparticle to be $d_U=d/2+\sqrt{d^2+4}/2$ and ensures that the corresponding propagator has zeros with $d$ the spacetime dimension of the unparticle field. Should $d=2+1$, unparticles acquire the non-trivial phase $2\pi d_U$ upon interchange. Because $d_U$ is non-integer and in general not half-integer, clockwise and counterclockwise interchange of unparticles do not lead to the same phase and time reversal symmetry is broken spontaneously as reported in numerous experiments in the pseudogap phase of the cuprates. The possible relevance of this mechanism to such experiments is discussed. We then formulate the analogous BCS gap using unparticles and find that in contrast to the Fermi liquid case, the transition temperature increases as the attractive interaction strength decreases, indicating that unparticles are highly susceptible to a superconducting instability.

10 pages 2 figures: Updated version to appear in Phys. Rev. B

References in corpus (19)

• Unparticle Physics
• Magnetic order in the pseudogap phase of high-$T_C$ superconductors
• Polar Kerr Effect Measurements of YBa2Cu3O6+x: Evidence for Broken Symmetry Near the Pseudogap Temperature
• A Phenomenological Theory of The Pseudogap State
• Unconventional critical behaviour in a quasi-two-dimensional organic conductor
• Deconstruction of Unparticles
• On the Reconstructed Fermi Surface in the Underdoped Cuprates
• Measurement of x-ray absorption spectra of overdoped high-temperature cuprate superconductors: Inapplicability of the single-band Hubbard model
• Kerr effect as evidence of gyrotropic order in the cuprates
• Absence of Luttinger's Theorem due to Zeros in the Single-Particle Green Function
• Strongly Correlated Topological Superconductors and Topological Phase Transitions via Green's Function
• Berry phase mechanism for optical gyrotropy in stripe-ordered cuprates
• Composite-Fermion Theory for Pseudogap, Fermi Arc, Hole Pocket, and Non-Fermi-Liquid of Underdoped Cuprate Superconductors
• Unparticle as a field with continuously distributed mass
• Hidden Charge 2e Boson in Doped Mott Insulators: Field Theory of Mottness
• Universal quantum criticality at the Mott-Anderson transition
• Exact Integration of the High Energy Scale in Doped Mott Insulators
• Unparticle Realization Through Continuous Mass Scale Invariant Theories
• Unparticle-Higgs Mixing: MSW Resonances, See-saw Mechanism and Spinodal Instabilities

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• Fractional Electromagnetism in Quantum Matter and High-Energy Physics
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• Characterizing Featureless Mott Insulating State by Quasiparticle Interferences - A Dynamical Mean Field Theory Prospect
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• Landau Quasiparticles in Weak Power-Law Liquids
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