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[1] 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 as an action in anti de Sitter space which serves as the generating functional for the propagator. We find that this mapping fixes the scaling dimension of the unparticle to be dU = d/2 + √ 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 2πdU upon interchange. Because dU 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.

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.…”

“…The condition for the superconducting instability is the divergence of the pair susceptibitliy. In the ladder approximation, such a condition is given by the equation, To understand more about the behavior of the solution to this equation, we calculate the beta function dg d ln T [18,30]. We scale outT ≡ T W .…”

Beyond Particles: Unparticles in Strongly Correlated Electron Matter

“…As a result, we have advocated then that unparticles provide a description of the incoherent fermionic contribution to the charge density in the pseudo gap and strange metal regions of the cuprates 31 . Since all formulations of superconductivity start with well-defined quasiparticles, we explore what happens when we use a quasiparticle spectral function with a scaling form indicative of unparticles.…”

Realizing infrared power-law liquids in the cuprates from unparticle interactions

“…In other words, unparticles arise from integrating out the high energy degrees of freedom of a generic field theory. In the context of the cuprates, one of us 16 has proposed that unparticle stuff can describe the pseudogap phase, in which the excitations are not adiabatically connected to Fermi liquids. Furthermore, the infrared properties of these excitations must be controlled by a strong coupling critical fixed point.…”