Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical review. B, Condensed matter

Spin-charge-separated Luttinger liquid in a magnetic field

Krzysztof Byczuk

Published Feb 15, 1998• 3 citations
Publisher

Abstract

The spin-charge-separated Luttinger liquid in arbitrary spatial dimensions and in the applied external magnetic field is investigated within an exactly solvable model of correlated fermions. Exact eigenstates, eigenvalues, and correlation functions of this system are determined and its single-pseudoparticle properties are discussed. It is shown that strongly correlated fermions of spin one-half and charge one, which are described by the present model, can be mapped onto a system of noninteracting fermionlike pseudoparticles possessing continuous charge and spin. The charge and the spin of these pseudoparticles acquire arbitrary values between 0 and $e$ and 0 and $\ensuremath{\Elzxh}/2$, respectively, when the magnetic field is varied. These pseudoparticles represent quanta of exact elementary excitations in this system.

DOI
10.1103/physrevb.57.3821

Related papers

Generalized hard-core fermions in one dimension: An exactly solvable Luttinger liquid

G. Gómez-Santos

A model for interacting spinless fermions in one dimension is presented and solved exactly. The solution is shown to be a Luttinger liquid with charge density wave instabilities for well characterized filling factors. Under very plausible assumptions, the exact solution is extended to the spin case with the usual charge-spin separation into two different Luttinger liquids. Required technicalities are almost trivial but the solution is very rich: Periodicity of instabilities and correlation exponents can be chosen at will.

Physical Review Letters•Jun 14, 1993•30 citations

Generalization of the Landau liquid concept: example of the Luttinger liquids

J. M. P. Carmelo, Alexander A. Ovchinnikov

The authors introduce a new representation of the Bethe ansatz solutions for 1D Luttinger liquids which describes the spectral properties and asymptotic behaviour of the correlation functions of the 1D Hubbard model in terms of the renormalized interaction of charge and spin pseudoparticles. The study of the low-lying eigenstates is reduced to the familiar languages of band theory and of the Fermi liquid. The authors results provide a better understanding of the decoupling of charge and spin degrees of freedom in 1D interacting systems, generalize the concept of a Landau liquid and may be relevant to the physics of higher dimensional systems.

Journal of Physics Condensed Matter•Feb 11, 1991•29 citations

Generalization of the Landau liquid concept: example of the Luttinger liquids

J. M. P. Carmelo, Alexander A. Ovchinnikov

The authors introduce a new representation of the Bethe ansatz solutions for 1D Luttinger liquids which describes the spectral properties and asymptotic behaviour of the correlation functions of the 1D Hubbard model in terms of the renormalized interaction of charge and spin pseudoparticles. The study of the low-lying eigenstates is reduced to the familiar languages of band theory and of the Fermi liquid. The authors results provide a better understanding of the decoupling of charge and spin degrees of freedom in 1D interacting systems, generalize the concept of a Landau liquid and may be relevant to the physics of higher dimensional systems.

Advanced series in mathematical physics•May 1, 1994•0 citations

Colloquium: The spin-incoherent Luttinger liquid

Gregory A. Fiete

In contrast to the well-known Fermi-liquid theory of three dimensions, interacting one-dimensional and quasi-one-dimensional systems of fermions are described at low energy by an effective theory known as Luttinger liquid theory. This theory is expressed in terms of collective many-body excitations that show exotic behavior such as spin-charge separation. Luttinger liquid theory is commonly applied on the premise that ``low energy'' describes both the spin and charge sectors. However, when the interactions in the system are very strong, as they typically are at low particle densities, the ratio of spin to charge energy may become exponentially small. It is then possible at very low temperatures for the single-spin excitation energy to be low compared to the characteristic single excitation charge energy, but still high compared to the characteristic spin energy. This energy window of near ground-state charge degrees of freedom but highly thermally excited spin degrees of freedom is called a spin-incoherent Luttinger liquid. The spin-incoherent Luttinger liquid exhibits a higher degree of universality than the Luttinger liquid and its properties are qualitatively distinct. In this Colloquium some recent theoretical developments in the field are detailed and experimental indications of such a regime in gated semiconductor quantum wires are described.

arXiv:cond-mat/0611597•Reviews of Modern Physics•Jul 13, 2007•145 citations

Beyond Fermi-Liquid Theory: the kkk-Fermi liquids

Tai Kai Ng

We study in this paper the general properties of a many body system of fermions in arbitrary dimensions assuming that the {\em momentum} of individual fermions are good quantum numbers of the system. We call these systems $k$-Fermi liquids. We show how Fermi liquid, Luttinger liquid (or Fermi liquid with exclusion statistics) and spin-charge separation arises from this framework. Two exactly solvable $k$-Fermi liquid models with spin-charge separation are discussed as examples.

arXiv:1910.06602•Oct 15, 2019•0 citations

Charge-spin separation and the spectral properties of Luttinger liquids

Johannes Voit

We compute the spectral function \ensuremath{\rho}(q,\ensuremath{\omega}) of the one-dimensional Luttinger model. Charge-spin separation gives spectral weight at frequencies between the charge and spin-fluctuation dispersions while spectral weight above ${\mathit{v}}_{\mathrm{\ensuremath{\rho}}}$q and below -${\mathit{v}}_{\mathrm{\ensuremath{\rho}}}$q is related to the anomalous dimensions of the fermion operators. The generalization of these results to many-particle correlations is discussed as well as the possibilities for their experimental verification in quasi-one-dimensional conductors.

Physical review. B, Condensed matter•Mar 15, 1993•231 citations
The spin-charge-separated Luttinger liquid in arbitrary spatial dimensions and in the applied external magnetic field is investigated within an exactly solvable model of correlated fermions. Exact eigenstates, eigenvalues, and correlation functions of this system are determined and its single-pseudoparticle properties are discussed. It is shown that strongly correlated fermions of spin one-half and charge one, which are described by the present model, can be mapped onto a system of noninteracting fermionlike pseudoparticles possessing continuous charge and spin. The charge and the spin of these pseudoparticles acquire arbitrary values between 0 and eee and 0 and \ensuremath\Elzxh/2\ensuremath{\Elzxh}/2\ensuremath\Elzxh/2, respectively, when the magnetic field is varied. These pseudoparticles represent quanta of exact elementary excitations in this system.
A model for interacting spinless fermions in one dimension is presented and solved exactly. The solution is shown to be a Luttinger liquid with charge density wave instabilities for well characterized filling factors. Under very plausible assumptions, the exact solution is extended to the spin case with the usual charge-spin separation into two different Luttinger liquids. Required technicalities are almost trivial but the solution is very rich: Periodicity of instabilities and correlation exponents can be chosen at will.
The authors introduce a new representation of the Bethe ansatz solutions for 1D Luttinger liquids which describes the spectral properties and asymptotic behaviour of the correlation functions of the 1D Hubbard model in terms of the renormalized interaction of charge and spin pseudoparticles. The study of the low-lying eigenstates is reduced to the familiar languages of band theory and of the Fermi liquid. The authors results provide a better understanding of the decoupling of charge and spin degrees of freedom in 1D interacting systems, generalize the concept of a Landau liquid and may be relevant to the physics of higher dimensional systems.
The authors introduce a new representation of the Bethe ansatz solutions for 1D Luttinger liquids which describes the spectral properties and asymptotic behaviour of the correlation functions of the 1D Hubbard model in terms of the renormalized interaction of charge and spin pseudoparticles. The study of the low-lying eigenstates is reduced to the familiar languages of band theory and of the Fermi liquid. The authors results provide a better understanding of the decoupling of charge and spin degrees of freedom in 1D interacting systems, generalize the concept of a Landau liquid and may be relevant to the physics of higher dimensional systems.
In contrast to the well-known Fermi-liquid theory of three dimensions, interacting one-dimensional and quasi-one-dimensional systems of fermions are described at low energy by an effective theory known as Luttinger liquid theory. This theory is expressed in terms of collective many-body excitations that show exotic behavior such as spin-charge separation. Luttinger liquid theory is commonly applied on the premise that ``low energy'' describes both the spin and charge sectors. However, when the interactions in the system are very strong, as they typically are at low particle densities, the ratio of spin to charge energy may become exponentially small. It is then possible at very low temperatures for the single-spin excitation energy to be low compared to the characteristic single excitation charge energy, but still high compared to the characteristic spin energy. This energy window of near ground-state charge degrees of freedom but highly thermally excited spin degrees of freedom is called a spin-incoherent Luttinger liquid. The spin-incoherent Luttinger liquid exhibits a higher degree of universality than the Luttinger liquid and its properties are qualitatively distinct. In this Colloquium some recent theoretical developments in the field are detailed and experimental indications of such a regime in gated semiconductor quantum wires are described.
We study in this paper the general properties of a many body system of fermions in arbitrary dimensions assuming that the {\em momentum} of individual fermions are good quantum numbers of the system. We call these systems kkk-Fermi liquids. We show how Fermi liquid, Luttinger liquid (or Fermi liquid with exclusion statistics) and spin-charge separation arises from this framework. Two exactly solvable kkk-Fermi liquid models with spin-charge separation are discussed as examples.
We compute the spectral function \ensuremath{\rho}(q,\ensuremath{\omega}) of the one-dimensional Luttinger model. Charge-spin separation gives spectral weight at frequencies between the charge and spin-fluctuation dispersions while spectral weight above ${\mathit{v}}_{\mathrm{\ensuremath{\rho}}}$q and below -${\mathit{v}}_{\mathrm{\ensuremath{\rho}}}$q is related to the anomalous dimensions of the fermion operators. The generalization of these results to many-particle correlations is discussed as well as the possibilities for their experimental verification in quasi-one-dimensional conductors.