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arXiv:cond-mat/9803134

Chiral Liquids in 1-d: A New Class of NFL-Fixed Points

Natan Andrei, Michael R. Douglas, Andrés Jerez

Published Mar 11, 1998• 0 citations
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Abstract

We identify a non Fermi Liquid (NFL) class of fixed points describing the infrared behaviour of interacting chiral fermions in one dimension. The thermodynamic properties and asymptotic correlation functions are characterized by universal exponents, which we determine by means of conformal and Bethe-Ansatz techniques. The mechanism leading to the breakdown of Fermi-Liquid theory is quite general and can be expected to be realized in systems with broken T-invariance. As an example we study the edge states of interacting QHE systems. We calculate the universal frequency dependence of the spin conductance in these systems as well as the NMR response.

DOI
10.48550/arxiv.cond-mat/9803134

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We identify a non Fermi Liquid (NFL) class of fixed points describing the infrared behaviour of interacting chiral fermions in one dimension. The thermodynamic properties and asymptotic correlation functions are characterized by universal exponents, which we determine by means of conformal and Bethe-Ansatz techniques. The mechanism leading to the breakdown of Fermi-Liquid theory is quite general and can be expected to be realized in systems with broken T-invariance. As an example we study the edge states of interacting QHE systems. We calculate the universal frequency dependence of the spin conductance in these systems as well as the NMR response.
We identify a non-Fermi-liquid class of fixed points describing the infrared behavior of interacting chiral fermions in one dimension. The thermodynamic properties and asymptotic correlation functions are characterized by universal exponents, which we determine by means of conformal and Bethe Ansatz techniques. The mechanism leading to the breakdown of Fermi-liquid theory is quite general and can be expected to be realized in systems with broken T invariance. As an example we study the edge states of interacting quantum Hall effect systems, where we calculate the universal NMR response.
We study models of chiral interacting fermions by means of conformal and Bethe-Ansatz techniques, and determine their thermodynamic properties and asymptotic correlation functions. We identify a class of fixed points characterizing the infrared behavior of the models. They display {\it chirally stabilized} non Fermi-Liquid behavior characterized by universal exponents. A realization of these fluids may be found in the edge states of bilayered QHE systems. We calculate the universal temperature dependence of the staggered conductance in these systems.
A variety of exotic non-Fermi liquid (NFL) states have been observed in many condensed matter systems, with different scaling relations between transport coefficients and temperature. The ``standard'' approach to studying these NFLs is by coupling a Fermi liquid to quantum critical fluctuations, which potentially can drive the system into a NFL. In this work we seek for an alternative understanding of these various NFLs in a unified framework. We first construct two ``elementary'' randomness-free models with four-fermion interactions only, whose many properties can be analyzed exactly in certain limit just like the Sachdev-Ye-Kitaev model. The most important new feature of our models is that, the fermion scaling dimension in the conformal invariant solution in the infrared limit is tunable by charge density. Then based on these elementary models, we propose two versions of lattice models with four-fermion interactions which give us non-Fermi liquid behaviors with dc resistivity scaling $\ensuremath{\varrho}\ensuremath{\sim}{T}^{\ensuremath{\alpha}}$ in a finite-temperature window, and $\ensuremath{\alpha}\ensuremath{\in}[1,2)$ depends on the fermion density in the model, which is a rather universal feature observed in many experimental systems.
Significant effort has been devoted to the study of "non-Fermi-liquid" (NFL) metals: gapless conducting systems that lack a quasiparticle description. One class of NFL metals involves a finite density of fermions interacting with soft order parameter fluctuations near a quantum critical point. The problem has been extensively studied in a large-N limit (N corresponding to the number of fermion flavors) where universal behavior can be obtained by solving a set of coupled saddle-point equations. However, a remarkable study by Lee revealed the breakdown of such approximations in two spatial dimensions. We show that an alternate approach, in which the fermions belong to the fundamental representation of a global SU(N) flavor symmetry, while the order parameter fields transform under the adjoint representation (a "matrix large-N" theory), yields a tractable large N limit. At low energies, the system consists of an overdamped boson with dynamical exponent z=3 coupled to a non-Fermi-liquid with self-energy Σ(ω)∼ω^{2/3}, consistent with previous studies.
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.
The explicitly soluble Luttinger model is used as a basis for the description of the general interacting Fermi gas in one dimension, which will be called 'Luttinger liquid theory', by analogy with Fermi liquid theory. The excitation spectrum of the Luttinger model is described by density-wave, charge and current excitations; its spectral properties determine a characteristic parameter that controls the correlation function exponents. These relations are shown to survive in non-soluble generalisations of the model with a non-linear fermion dispersion. It is proposed that this low-energy structure is universal to a wide class of 1D systems with conducting or fluid properties, including spin chains.