Luttinger" and insulating spin liquids in two dimensions (original) (raw)

Curvature and Truncation for a Flat Fermi Surface

2003

In the present work, we implement an explicit two-loop renormalization of a two-dimensional flat Fermi surface (FS) in the framework of a field theoretical renormalization group (RG) approach. In our scheme, we derive the RG equations for both coupling functions and Fermi energy. In this way, we are able to probe the existence of spin-charge separation by showing that the low-energy sector of the system is in fact a non-Fermi liquid. In addition, associating the true interacting FS to the infrared stable (IR) fixed point of the Fermi energy, we demonstrate here that it either acquires a small curvature and behaves as a "Luttinger liquid" or it suffers a truncation in k-space depicting an insulating spin liquid.

Field-theoretical renormalization group for a flat two-dimensional Fermi surface

Physical Review B, 2005

We implement an explicit two-loop calculation of the coupling functions and the self-energy of interacting fermions with a two-dimensional flat Fermi surface in the framework of the field theoretical renormalization group (RG) approach. Throughout the calculation both the Fermi surface and the Fermi velocity are assumed to be fixed and unaffected by interactions. We show that in two dimensions, in a weak coupling regime, there is no significant change in the RG flow compared to the well-known one-loop results available in the literature. However, if we extrapolate the flow to a moderate coupling regime there are interesting new features associated with an anisotropic suppression of the quasiparticle weight Z along the Fermi surface, and the vanishing of the renormalized coupling functions for several choices of the external momenta.

Non-Fermi liquid in a truncated two-dimensional Fermi surface

Physical Review B, 2003

Using perturbation theory and the field theoretical renormalization group approach we consider a two-dimensional anisotropic truncated Fermi Surface(F S) with both flat and curved sectors which approximately simulates the "cold" and "hot" spots in the cuprate superconductors. We calculate the one-particle two-loop irreducible functions Γ (2) and Γ (4) as well as the spin, the charge and pairing response functions up to one-loop order. We find non-trivial infrared stable fixed points and we show that there are important effects produced by the mixing of the existing scattering channels in higher order of perturbation theory. Our results indicate that the "cold " spots are turned into a non-Fermi liquid with divergents ∂Σ0/∂p0 and ∂Σ0/∂p, a vanishing Z and a finite Fermi velocity at F S when the effects produced by the flat portions are taken into account.

Fermi surface renormalization in two dimensions

Physica C: Superconductivity, 2004

We investigate a two-dimensional totally flat Fermi surface (FS) model using a two-loop field theoretical renormalization group (RG) approach. We take full account of the FS renormalization calculating explicitly how the RG equations for the renormalized chemical potential (l R ) and coupling functions vary with the parallel momentum (p k ) along the Fermi surface. We find non-trivial infrared (IR) stable fixed points for the couplings of the model for any choice of p k . In our scheme, the true interacting Fermi surface is directly related to the IR stable fixed point of the renormalized chemical potential. In this way, we show that the renormalized FS develops a small curvature and becomes truncated as a result of interactions.

Fermi liquid parameters in two dimensions with spin-orbit interaction

Physical Review B, 2005

We derive analytical expressions for the quasiparticle lifetime τ , the effective mass m * , and the Green's function renormalization factor Z for a 2D Fermi liquid with electron-electron interaction in the presence of the Rashba spin-orbit interaction. We find that the modifications are independent of the Rashba band index ρ, and occur in second order of the spin-orbit coupling α. In the derivation of these results, we also discuss the screening of the Coulomb interaction, as well as the susceptibility and the self-energy in small α.

Marginal Fermi Liquid with a Two-Dimensional Patched Fermi Surface

Modern Physics Letters B, 1999

We consider a model composed of Landau quasiparticle states with patched Fermi surfaces (FS) sandwiched by states with flat FS to simulate the "cold" spot regions in cuprates. We calculate the one-particle irreducible function and the self-energy up to two-loop order. Using renormalization group arguments, we show that in the forward scattering channel, the renormalized coupling constant is never infrared stable due to the flat FS sectors. Furthemore, we show that the self-energy scales with energy as Re ∑~ω ln ω as ω→0, and thus the Fermi liquid state within each FS patch is turned into a marginal Fermi liquid.

Renormalization group for two-dimensional fermions with a flat Fermi surface

Physical Review B, 2002

We present a renormalization group analysis of two-dimensional interacting fermion systems with a closed and partially flat Fermi surface. Numerical solutions of the one-loop flow equations show that for a bare local repulsion, the system evolves through three different regimes as the typical energy is lowered : a high-energy transient with a strong competition between particle-particle and particle-hole channels, an intermediate regime with dominant spin density wave correlations, and finally a "hot spot" regime exhibiting d-wave superconductivity. We study, mostly by analytical methods, how this flow pattern depends on the number N of Fermi surface patches used in the numerical solution. This clearly indicates that the final regime requires vanishingly small microscopic interactions, for the one-loop approximation to be valid, as N is going to infinity.

Luttinger liquid fixed point for a two-dimensional flat Fermi surface

Physical Review B, 2008

We consider a system of 2D interacting fermions with a flat Fermi surface. The apparent conflict between Luttinger and non Luttinger liquid behavior found through different approximations is resolved by showing the existence of a line of non trivial fixed points, for the RG flow, corresponding to Luttinger liquid behavior; the presence of marginally relevant operators can cause flow away from the fixed point. The analysis is non-perturbative and based on the implementation, at each RG iteration, of Ward Identities obtained from local phase transformations depending on the Fermi surface side, implying the partial vanishing of the Beta function.

Marginal Fermi liquid behavior from 2d Coulomb interaction

A full, nonperturbative renormalization group analysis of interacting electrons in a graphite layer is performed, in order to investigate the deviations from Fermi liquid theory that have been observed in the experimental measures of a linear quasiparticle decay rate in graphite. The electrons are coupled through Coulomb interactions, which remain unscreened due to the semimetallic character of the layer. We show that the model flows towards the noninteracting fixed-point for the whole range of couplings, with logarithmic corrections which signal the marginal character of the interaction separating Fermi liquid and non-Fermi liquid regimes. 71.27.+a, 73.20.Dx, 05.30.Fk During recent years there has been important progress in understanding the properties of quantum electron liquids in dimension D < 3. One of the most fruitful approaches in this respect springs from the use of renormalization group (RG) methods, in which the different liquids are characterized by several fixed-points controlling the low-energy properties. The Landau theory of the Fermi liquid in dimension D > 1 can be taken as a paradigm of the success of this program. It has been shown that, at least in the continuum limit, a system with isotropic Fermi surface and regular interactions is susceptible of developing a fixed-point in which the interaction remains stable in the infrared 1 .