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arXiv:hep-th/9510058 · Physical review. B, Condensed matter

Deviations from Fermi-liquid behavior in (2+1)-dimensional quantum electrodynamics and the normal phase of high- Tc superconductors

I. J. R. Aitchison, Nick E. Mavromatos

Published Apr 1, 1996• 58 citations
arXivHTMLPDF

Abstract

We argue that the gauge-fermion interaction in multiflavor quantum electrodynamics in (2+1) dimensions is responsible for non-Fermi-liquid behavior in the infrared, in the sense of leading to the existence of a nontrivial (quasi)fixed point that lies between the trivial fixed point (at infinite momenta) and the region where dynamical symmetry breaking and mass generation occurs. This quasifixed-point structure implies slowly varying, rather than fixed, couplings in the intermediate regime of momenta, a situation which resembles that of (four-dimensional) "walking technicolor" models of particle physics. The inclusion of wave-function renormalization yields marginal $O(\frac{1}{N})$ corrections to the "bulk" non-Fermi-liquid behavior caused by the gauge inter-action in the limit of infinite flavor number. Such corrections lead to the appearance of modified critical exponents. In particular, at low temperatures there appear to be logarithmic scaling violations of the linear resistivity of the system of order $O(\frac{1}{N})$. The connection with the anomalous normal-state properties of certain condensed-matter systems relevant for high-temperature superconductivity is briefly discussed. The relevance of the large (flavor) $N$ expansion to the Fermi-liquid problem is emphasized. As a partial result of our analysis, we point out the absence of charge-density-wave instabilities from the effective low-energy theory, as a consequence of gauge invariance.

DOI
10.1103/physrevb.53.9321

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We argue that the gauge-fermion interaction in multiflavor quantum electrodynamics in (2+1) dimensions is responsible for non-Fermi-liquid behavior in the infrared, in the sense of leading to the existence of a nontrivial (quasi)fixed point that lies between the trivial fixed point (at infinite momenta) and the region where dynamical symmetry breaking and mass generation occurs. This quasifixed-point structure implies slowly varying, rather than fixed, couplings in the intermediate regime of momenta, a situation which resembles that of (four-dimensional) "walking technicolor" models of particle physics. The inclusion of wave-function renormalization yields marginal O(1N)O(\frac{1}{N})O(N1​) corrections to the "bulk" non-Fermi-liquid behavior caused by the gauge inter-action in the limit of infinite flavor number. Such corrections lead to the appearance of modified critical exponents. In particular, at low temperatures there appear to be logarithmic scaling violations of the linear resistivity of the system of order O(1N)O(\frac{1}{N})O(N1​). The connection with the anomalous normal-state properties of certain condensed-matter systems relevant for high-temperature superconductivity is briefly discussed. The relevance of the large (flavor) NNN expansion to the Fermi-liquid problem is emphasized. As a partial result of our analysis, we point out the absence of charge-density-wave instabilities from the effective low-energy theory, as a consequence of gauge invariance.
We introduce a Hamiltonian coupled between a normal Fermi surface and a polarized Maxwell type gauge field.We adopt a {\it calibrated scaling } approach in order to be consistent with the results obtained at 2+12+12+1 dimensions as well as the Weinberg's theo rem. Renormalization group equations are calculated by using a dimension regulator. It turns out that the gauge interaction is controlled by a non-trivial fixed point. The two-point Green's function can thus be calculated accurately in the low temperature limit and possesses a non-quasi particle pole which signals the break down of the Landau Fermi liquid theory. In addition,we show that the anomalous dimension of fermion field is in general gauge dependent. But it will survive under generic gauge choice due to the renormalization of the gauge fixing parameter.
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We study a dissipative gauge theory of nonrelativistic fermions in 2+1 dimensions at zero temperature by the Wilsonian renormalization-group method. In this theory, we incorporate in the fermion propagator a new term of the form $ i κ\cdot\sign(ω)$ (where κκκ is a parameter and ωωω is the fermion frequency), which is usually induced by impurity effects. In the previous papers, we studied this system for κ=0κ= 0κ=0, and showed that there exists a non-Fermi-liquid infrared fixed point. In this paper, we address the question whether this non-Fermi-liquid behavior remains stable or not in the presence of impurity effects, i.e., the κκκ term. Our results show that the non-Fermi-liquid fixed point is unstable for κ≠0κ\neq 0κ=0 and an effective gauge coupling constant tends to vanish at low energies. However, in intermediate energy scales, the behavior of correlation functions for κ≠0κ\neq 0κ=0 is controlled by the non-Fermi-liquid fixed point at κ=0κ=0κ=0, i.e., a crossover phenomenon appears. Physical implications of this phenomenon are discussed.
In metals, low-energy effective theories are characterized by a set of coupling functions. Among them, the angle-dependent Fermi momentum specifies the size and shape of Fermi surface. Since the Fermi momentum grows incessantly under the renormalization group flow, a metallic fixed point is defined only modulo a rescaling of Fermi momentum. In this paper, we discuss the physical consequences of this projective nature of fixed points for non-Fermi liquids with hot Fermi surfaces. The first is the absence of a unique dynamical critical exponent that dictates the relative scaling between energy and momentum. The second is mismatches between the scaling dimensions of couplings and their relevancy. Nonetheless, each projective fixed point is characterized by a few marginal and relevant coupling functions, and the notion of universality survives. We illustrate our findings by charting the space of projective fixed points and extracting their universal properties for the Ising-nematic quantum critical metal beyond the patch theory. To control the theory, we use the dimensional regularization scheme that tunes the co-dimension of Fermi surface. Near the upper critical dimension, two exactly marginal coupling functions span the space of stable projective fixed points: functions that specify the shape of the Fermi surface and the angle-dependent Fermi velocity. All other coupling functions, including the Landau functions and the universal pairing interaction, are fixed by those two marginal functions. With decreasing dimensions, the forward scattering remains irrelevant while the pairing interaction becomes relevant near two dimensions. In two dimensions, it is expected that the universal superconducting fluctuations lower the symmetry of the non-Fermi liquid realized above the superconducting transition temperatures from the loop U(1) group to a proper subgroup.
Role of quenched randomness in metallic quantum criticality is one of the long standing problems in condensed matter physics. An aspect of the fundamental difficulties lies in the fact that such nonmagnetic disorders lead effective interactions between abundant soft modes near the Fermi surface to be drastically enhanced particularly in the diffusive regime, where the perturbative framework does not work. Here, we revisit the problem of dirty quantum critical metals in a different angle, focusing on the hydrodynamic regime instead of the diffusive regime near the non-Fermi liquid quantum critical point. More concretely, we study effects of mutual correlations between quantum critical nematic fluctuations and weak localization corrections, and show the existence of a weak-disorder non-Fermi liquid fixed point, based on the renormalization group (RG) analysis up to the two-loop order. The two-loop order RG analysis suggests that the absence of quantum coherence in two-particle composite excitations weakens the role of weak localization corrections and allows a weakly disordered non-Fermi liquid metallic state in the hydrodynamic regime of the nematic quantum critical point. Although this dirty non-Fermi liquid metallic state may not be the true infrared stable fixed point at zero temperature, expected to be characterized by the diffusive Ohmic regime, we argue that this weak-disorder non-Fermi liquid metallic fixed point would govern the region of an intermediate energy scale, described by effective hydrodynamics of nematic quantum criticality. In this respect we believe that this research would be an important step in understanding the T−T-T−linear electrical resistivity as a characteristic feature of non-Fermi liquids and the origin of unconventional superconductivity from effective hydrodynamics of quantum criticality.
Since the mid-eighties there has been an accumulation of metallic materials whose thermodynamic and transport properties differ significantly from those predicted by Fermi liquid theory. Examples of these so-called non-Fermi liquids include the strange metal phase of high transition temperature cuprates, and heavy fermion systems near a quantum phase transition. We report on a class of non-Fermi liquids discovered using gauge/gravity duality. The low energy behavior of these non-Fermi liquids is shown to be governed by a nontrivial infrared (IR) fixed point which exhibits nonanalytic scaling behavior only in the temporal direction. Within this class we find examples whose single-particle spectral function and transport behavior resemble those of strange metals. In particular, the contribution from the Fermi surface to the conductivity is inversely proportional to the temperature. In our treatment these properties can be understood as being controlled by the scaling dimension of the fermion operator in the emergent IR fixed point.