Theory of Non-Fermi Liquids

D. ter Haar

Sung-Sik Lee

Non-Fermi liquids are unconventional metals whose physical properties deviate qualitatively from those of noninteracting fermions due to strong quantum fluctuations near Fermi surfaces. They arise when metals are subject to singular interactions mediated by soft collective modes. In the absence of well-defined quasiparticles, universal physics of non-Fermi liquids is captured by interacting field theories which replace Landau Fermi liquid theory. However, it has been difficult to understand their universal low-energy physics due to a lack of theoretical methods that take into account strong quantum fluctuations in the presence of abundant low-energy degrees of freedom. In this review, we discuss two approaches that have been recently developed for non-Fermi liquid theory with emphasis on two space dimensions. The first is a perturbative scheme based on a dimensional regularization, which achieves a controlled access to the low-energy physics by tuning the codimension of Fermi surface. The second is a nonperturbative approach which treats the interaction ahead of the kinetic term through a non-Gaussian scaling called interaction-driven scaling. Examples of strongly coupled non-Fermi liquids amenable to exact treatments through the interaction-driven scaling are discussed.

Григорий Ефимович Воловик

In the fermionic liquids, the Fermi surface is topologically stable,\cite{Volovik2003} which is at the origin of the applicability of the Landau theory of Fermi liquid (LFL). The LFL exists under special condition, when the Green's function has a pole with nonzero residue $Z$. Otherwise one has non-Landau Fermi liquid (NLFL), such as Luttinger liquid, which is described by the same topological invariant. It appears that in general this topological invariant is the property of the fermionic particle, i.e. the particle charge (or the electric charge of electron) is equivalent to the topological charge of the fermion. The conservation of the fermionic charge is equivalent to the conservation of the topological charge. We consider the application of this topological charge to the Landau theory of Fermi liquids. We also consider the application to non-Fermi liquids and crystalline insulators in relation to the Luttinger theorem.

Hiroshi Takano, Masaru Onoda, Ikuo Ichinose +1 more

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 $κ$ is a parameter and $ω$ is the fermion frequency), which is usually induced by impurity effects. In the previous papers, we studied this system for $κ= 0$, 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 $κ$ term. Our results show that the non-Fermi-liquid fixed point is unstable for $κ\neq 0$ and an effective gauge coupling constant tends to vanish at low energies. However, in intermediate energy scales, the behavior of correlation functions for $κ\neq 0$ is controlled by the non-Fermi-liquid fixed point at $κ=0$, i.e., a crossover phenomenon appears. Physical implications of this phenomenon are discussed.