Beyond Particles: Unparticles in Strongly Correlated Electron Matter

Abstract

I am concerned in these lectures with the breakdown of the particle concept in strongly correlated electron matter. I first show that the standard procedure for counting particles, namely Luttinger's theorem, breaks down anytime pole-like excitations are replaced by ones that have a divergent self-energy. Such a breakdown obtains in electronic systems whose pole-like excitations do not extend to the edge of the Brillouin zone, as in Fermi arcs in the cuprates. Since any non-trivial infrared dynamics in strongly correlated electron matter must be controlled by a critical fixed point, unparticles are the natural candidate to explain the presence of charged degrees of freedom that have no particle content. The continuous mass formulation of unparticles is recast as an action in anti de Sitter space. Such an action serves as the generating functional for the propagator. This mapping fixes the scaling dimension of the unparticle to be d U = d/2 + √ d 2 + 4/2 and ensures that the corresponding propagator has zeros with d the spacetime dimension of the unparticle field. The general dynamical mechanism by which bulk operators, such as the Pauli term, couple to the scaling dimension of the boundary operator and thereby lead to a vanishing of the spectral weight at zero energy is reviewed in the context of unparticles and zeros. The analogue of the BCS gap equations with unparticles indicates that the transition temperature increases as the attractive interaction strength decreases, indicating that unparticles are highly susceptible to a superconducting instability.

Unparticles and anomalous dimensions in the cuprates

“…The scaling emerges from an interplay between the various flavors; even if the individual flavors themselves exhibit scaling with canonical exponents the behavior of the system as a whole is very different from the behavior of the individual flavors. Phillips and co-workers [18,19] developed the continuous mass formulation of unparticles to address the general properties of the pseudo gap phase of the cuprates, whereas [20] referred to the same construction as a "multi-band model". The latter emphasizes the fact that different flavors can be thought of as different bands, with N standing for the number of bands in an energy region of interest.…”

“…In our previous work on superconducting instabilities in the presence of unparticles, we formulated the problem entirely in terms of the scaling dimension of the propagator [18,19]. No explicit mention was made of the mass-dependence of the charge, density of states, or band edge and hence no immediate connection could be made with the results from the scaling analysis of the AC and DC properties.…”

Multiband models for field theories with anomalous current dimension

“…This general idea that one can obtain a scale invariant theory by integrating over the mass parameter has also recently been exploited in [12,13] where it was used to construct an "unparticle" description of non-Fermi liquids.…”