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arXiv:cond-mat/0403144

A Novel Non-Fermi Liquid Ground State in One Dimension

Girish S. Setlur, HRI

Published Mar 4, 2004• 0 citations
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Abstract

We propose a new non-Fermi liquid ground state in one dimension that is not of the Luttinger type. It is the ground state of fermions interacting via a long range repulsive interaction in real space of the form $ V(x) = e^2/|x| $. We characterise it by computing the momentum distribution which is perfectly flat near the Fermi points signalling a radical departure from Luttinger liquid theory(and Fermi liquid theory). The dispersion of elementary excitations is found to be sublinear but gapless of the form $ v {} |q| {}[ Log[2k_{F}/|q| ]^{1/2} $. We also compute the conductance of a mesoscopic wire made of such objects and contrast it from the answer we obtain for a Luttinger wire.

DOI
10.48550/arxiv.cond-mat/0403144

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We propose a new non-Fermi liquid ground state in one dimension that is not of the Luttinger type. It is the ground state of fermions interacting via a long range repulsive interaction in real space of the form V(x)=e2/∣x∣V(x) = e^2/|x|V(x)=e2/∣x∣. We characterise it by computing the momentum distribution which is perfectly flat near the Fermi points signalling a radical departure from Luttinger liquid theory(and Fermi liquid theory). The dispersion of elementary excitations is found to be sublinear but gapless of the form v∣q∣[Log[2kF/∣q∣]1/2v {} |q| {}[ Log[2k_{F}/|q| ]^{1/2}v∣q∣[Log[2kF​/∣q∣]1/2. We also compute the conductance of a mesoscopic wire made of such objects and contrast it from the answer we obtain for a Luttinger wire.
Fermions interacting via a long-range repulsive potential are considered in D spatial dimensions, where 1D\ensuremath{\le}2. The standard screening picture is found to break down, i.e., the screened effective interaction cannot be treated as instantaneous. For a bare potential which behaves at long distances as ${\mathit{r}}^{\mathrm{\ensuremath{-}}(2\mathrm{\ensuremath{-}}\mathit{D})}$ [as ln r in two dimensions (2D)] and within the random-phase approximation, the retardation effects induce an infrared catastrophe that changes the Fermi liquid into a Luttinger liquid in which the occupation number in momentum space is continuous across the Fermi surface. In 2D, the quantum liquid which we investigate may be called a ``Z=0 Fermi liquid'' (where Z is the strength of the quasiparticle pole at the Fermi surface) since the electron propagator has an isolated pole with a constant residue that scales to zero as the size of the system increases to infinity. For 1D2, the quantum liquid resembles the 1D Luttinger liquid as the single-particle propagator exhibits a branch cut structure. Moreover, we present a ground-state wave function which reproduces the Luttinger-liquid exponent of the momentum distribution near the Fermi surface.
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.
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.
We present a study of a gas of bosons confined in one dimension with Feshbach-resonant interactions, at zero temperature. Unlike the gas of one-dimensional bosons with non resonant interactions, which is known to be equivalent to a system of interacting spinless fermions and can be described using the Luttinger liquid formalism, the resonant gas possesses additional features. Depending on its parameters, the gas can be in one of three possible regimes. In the simplest of those, it can still be described by the Luttinger liquid theory, but its Fermi momentum cannot be larger than a certain cutoff momentum dependent on the details of the interactions. In the other two regimes, it is equivalent to a Luttinger liquid at low density only. At higher densities its excitation spectrum develops a minimum, similar to the roton minimum in helium, at momenta where the excitations are in resonance with the Fermi sea. As the density of the gas is increased further, the minimum dips below the Fermi energy, thus making the ground state unstable. At this point the standard ground state gets replaced by a more complicated one, where not only the states with momentum below the Fermi points, but also the ones with momentum close to that minimum, get filled, and the excitation spectrum develops several branches. We are unable so far to study this regime in detail due to the lack of the appropriate formalism.
The electronic systems in one dimension have features quite distinct from those in higher dimensions. The onedimensional Fermi surface consists of two discrete points, while in higher dimensions it is continuous. The low-energy particle-hole pairs’ spectrum, which arises from momentum and energy conservations for wave vector between zero and twice of Fermi wave vector does not exist in one dimension. In higher dimensions, this region of missing states is filled in. The Fourier transform of one-dimensional Coulomb potential diverges. This led to wide spread belief that one-dimensional interacting electronic systems should exhibit non-Fermi liquid (known as Luttinger liquid) behaviour. However, there is still no unambiguous evidence both for the real existence or non-existence of Luttinger liquid behaviour in a realistic quantum wire. This talk briefly reviews key aspects of Fermi liquid approach and Tomonaga-Luttinger liquid approach for a onedimensional system. In this paper, structure factor, pair distribution function and electron-electron scattering, which exhibit similarity between two approaches in low energy and momentum regime, is reviewed.
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.