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Physical review. B, Condensed matter

Metallic non-Fermi-liquid fixed point in two and higher dimensions

Xiao-Gang Wen

Published Oct 1, 1990• 180 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.42.6623

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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.
We study the problem of the crossover from one- to higher-dimensional metals by considering an array of Luttinger liquids (one-dimensional chains) coupled by a weak interchain hopping ${t}_{\ensuremath{\perp}}.$ We evaluate the exact asymptotic low-energy behavior of the self-energy in the anisotropic infinite-dimension limit. This limit extends the dynamical mean-field concept to the case of a chain embedded in a self-consistent medium. The system flows to a Fermi-liquid fixed point for energies below the dimensional crossover temperature, and the anomalous exponent \ensuremath{\alpha} renormalizes to zero, in the case of equal spin and charge velocities. In particular, the single-particle spectral function shows sharp quasiparticle peaks with nonvanishing weight along the whole Fermi surface, in contrast to the lowest-order result. Our result is obtained by carrying out a resummation of all diagrams of the expansion in ${t}_{\ensuremath{\perp}}$ contributing to the anisotropic $\stackrel{\ensuremath{\rightarrow}}{D}\ensuremath{\infty}$ limit. This is done by solving, in an almost completely analytic way, an asymptotically exact recursive equation for the renormalized vertices, within a skeleton expansion. Our outcome shows that perturbation expansions in ${t}_{\ensuremath{\perp}}$ restricted to lowest orders are unreliable below the crossover temperature. The extension to finite dimensions is discussed. This work extends our recent letter [Phys. Rev. Lett. 83, 128 (1999)], and includes all mathematical details.
We use higher-dimensional bosonization to study the normal state of electrons in weakly coupled metallic chains interacting with long-range Coulomb forces. Particular attention is paid to the crossover between Luttinger and Fermi-liquid behavior as the interchain hopping ${t}_{\ensuremath{\perp}}$ is varied. Although in the physically interesting case of finite but small ${t}_{\ensuremath{\perp}}$ the quasiparticle residue does not vanish, the single-particle Green's function exhibits the signature of Luttinger-liquid behavior (i.e., anomalous scaling and spin-charge separation) in a large intermediate parameter regime. Using realistic parameters, we find that the scaling behavior in this regime is characterized by an anomalous dimension of the order of unity, as suggested by recent experiments on quasi-one-dimensional conductors. Our calculation also gives insights into the approximations inherent in higher-dimensional bosonization; in particular, we show that the replacement of a curved Fermi surface by a finite number MMM of flat patches can give rise to unphysical nesting singularities in the single-particle Green's function, which disappear only in the limit $M\ensuremath{\rightarrow}\ensuremath{\infty}$ or if curvature effects are included. We also compare our approach with other methods. This work extends our recent letter [Phys. Rev. Lett. 74, 2997 (1995)].
The low-energy properties of interacting Fermi systems are highly constrained by conservation laws. They generally simplify the structure of the underlying renormalization group by reducing the number of independent renormalization constants. In one dimension, all properties of normal metallic fixed points are uniquely determined by separate charge and spin conservation for states near the left and right Fermi points, respectively. We construct the general Luttinger-liquid theory of one-dimensional (1D) metals directly from these conservation laws. Luttinger-liquid parameters emerge naturally from the velocities associated with the conserved currents at the Luttinger-liquid fixed point. Instead of bosonization, one may thus use techniques familiar from Fermi-liquid theory, i.e., Feynman diagrams, equations of motion, and Ward identities. The choice of a technique comprising both Fermi- and Luttinger-liquid theory makes the similarities and differences of both theories particularly transparent, and sets the stage for constructing non-Fermi-liquid metallic fixed points in d>1. Several generic properties and asymptotic conservation laws of 2D non-Fermi-liquid metals are discussed.
We analyze the low energy behavior of interacting fermions in continuous dimensions d between one and two. It is shown that Fermi liquid fixed points are stable with respect to residual scattering of quasiparticles by regular interactions in any dimension above one, while the structure of corrections to quasiparticle behavior changes drastically below two dimensions. The crossover from Luttinger liquid behavior in 1D to Fermi liquid behavior in higher dimensions is described by a tomographic Luttinger model with effective interactions approaching zero with a power d-1 of the distance from the Fermi surface.
Understanding non-Landau Fermi liquids in dimensions higher than one, has been a subject of great interest. Such phases may serve as parent states for other unconventional phases of quantum matter, in a similar manner that conventional broken symmetry states can be understood as instabilities of the Landau Fermi liquid. In this work, we investigate the emergence of a novel non-Landau Fermi liquid in two dimensions, where the fermions with quadratic band-touching dispersion interact with a Bose metal. The bosonic excitations in the Bose metal possess an extended nodal-line spectrum in momentum space, which arises due to the subsystem symmetry or the restricted motion of bosons. Using renormalization group analysis and direct computations, we show that the extended infrared (IR) singularity of the Bose metal leads to a line of interacting fixed points of novel non-Landau Fermi liquids, where the anomalous dimension of the fermions varies continuously, akin to the Luttinger liquid in one dimension. Further, the multi-patch generalization of the model is used to explore other unusual features of the resulting ground state.