Non-Fermi liquid fixed point in 2 + 1 dimensions

A. J. A. James, Austen Lamacraft

Ipsita Mandal

We consider the emergence of a non-Fermi liquid fixed point in two-dimensional metals at the onset of a quantum phase transition from a Fermi liquid state to an incommensurate charge density wave (CDW) ordered phase. The momentum of the CDW boson is centred at the wavevector Q, which connects a single pair of antipodal points on the Fermi surface with antiparallel tangent vectors. We employ the dimensional regularization technique in which the co-dimension of the Fermi surface is extended to a generic value, while keeping the dimension of Fermi surface itself fixed at one. Although the system is strongly coupled at dimension d=2, the interactions become marginal at the upper critical dimension d=dc, whose value is found to be 5/2. Using a controlled perturbative expansion in the parameter ϵ=dc−d, we compute the critical exponents of the stable infrared fixed point characterizing the quantum critical point. The scalings of the original theory are determined by setting ϵ=1/2, where the fermion self-energy is seen to scale with the frequency with a fractional power law of 2/3, which is the telltale signature of a typical non-Fermi liquid phase.

Subhro Bhattacharjee, Sung-Sik Lee, Yong Baek Kim

Xiao-Gang Wen

Quasi-one-dimensional electron systems in two and higher dimensions are studied. It is shown that the interchain electron hopping is renormalized to zero in the infrared limit if the intrachain repulsive interaction is strong enough. In this case the higher-dimensional electron system flows to metallic non-Fermi-liquid fixed points---a Luttinger liquid. Some experimental consequences, in particular the transport properties, of this infrared fixed point are studied. It would be interesting to observe this state in quasi-one-dimensional electron systems.

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.