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

Progress of Theoretical Physics Supplement

Luttinger Liquid in Two Dimensions: Fermionic Backflow and Transfer of Statistics

G. Baskaran

Published Jan 1, 1992• 2 citations
Publisher

Abstract

We discuss certain physical contents of the two-dimensional Luttinger liquid state using the spin and charge current backflow in strongly correlated electron systems. Also we attempt a description of the Luttinger liquid state in the slave boson formalism. Conventional slave boson mean field theory does not possess an important property expected of a Luttinger liquid, namely a pseudo fermi surface for holons. This arises from the bose condensation of holes. We attempt to rectify this by discussing the physics of the fermionic backflow associated with the hole motion. We argue that the fermionic backflow suppresses the Bose condensation. To understand this we introduce the notion of ‘Statistics Transfer’-the medium transfer certain statistics to the slave particle (e's). A variational wave function in which boson condensation is manifestly absent is introduced. The form of the wave function is justified by the concept of statistics transfer. The spinon and holon excitations both exhibiting pseudo fermi surfaces are constructed.

DOI
10.1143/ptps.107.49

Related papers

Luttinger Liquid in Two Dimensions--Fermionic Backflow and Transfer of Statistics (Low Dimensional Field Theories and Condensed Matter Physics(Proceedings of the 4th Yukawa International Seminar))

G. Baskaran

Progress of Theoretical Physics•May 1, 1992•0 citations

Non-Fermi liquid properties of two-dimensional electron systems.

Yujong Bai

We calculate the Green's function, particle-hole susceptibility and Cooper pair susceptibility of a 2D electron gas with long range current-current interactions, using Haldane bosonization scheme. We find Luttinger Liquid properties of weakly decaying power-law tails in the spectral function and a Kohn anomaly in the 2$k\sb{F}$ particle-hole susceptibility. At finite temperature, the system exhibits more radical departure from Fermi Liquid. The specific heat was determined being linearly proportional to temperature. The strong correlations of spins and holes are demonstrated in the 2D t-J model of spin-boson and hole-fermion, through the instability against charge ordering we find from our charge susceptibility calculation of bubble and ladder diagrams. We calculate the linear-T dependence of resistivity from the hole self-energy to the second order. The excitation spectra of holon and spinon found from the self-energy calculations agree with the mean-field results to that order.

•Jan 1, 1995•0 citations

U→∞ problem for a finite hole concentration: A bosonization approach for the normal-state high- Tc superconductors

D. Schmeltzer

The Hubbard model in the strong coupling limit is considered in two dimensions. A bosonization method based on the extention of the Jordan-Wigner transformation to particles with spin and no double occupancy is introduced. We find that at T=0 a Fermi liquid exists and superconductivity appears. For a finite temperature and finite doping a normal state populated with vortices exists. As a result, we have a normal state with separated charge- and spin-density-wave excitations. Formally those excitations can be described with the help of the Luttinger-liquid representation. In the second part we parametrize the Fermi surface by a set of N points. Around each point we describe the Fermi surface excitations by holons and spinons and find a set of N-coupled Luttinger channels. At T=0 we have space-time tunneling of electric charges which destroys the Luttinger liquid in favor of a Fermi liquid. At T\ensuremath{\ne}0 or LT\ensuremath{\rightarrow}\ensuremath{\infty} (L is the size of the system) tunneling of electric charges might be prohibited giving rise to gapless excitations. In the last part we consider the case with a commensurate frozen flux in the ground state. As a result we find that the excitations are semions.

Physical review. B, Condensed matter•Oct 1, 1993•4 citations

One-dimensional Fermi liquids

Johannes Voit

We review the progress in the theory of one-dimensional (ID) Fermi liquids which has occurred over the past decade. The usual Fermi liquid theory, based on a quasi-particle picture, breaks down in one dimension because of the Peierls divergence in the particle-hole bubble, producing anomalous dimensions of operators, and because of charge-spin separation. Both are related to the importance of scattering processes transferring finite momentum. A description of the low-energy properties of gapless 1D quantum systems can be based on the exactly solvable Luttinger model which incorporates these features, and whose correlation functions can be calculated. Special properties of the eigenvalue spectrum, parameterized by one renormalized velocity and one effective coupling constant per degree of freedom, fully describe the physics of this model. Other gapless 1D models share these properties in a low-energy subspace. The concept of a "Luttinger liquid" implies that their low-energy properties are described by an effective Luttinger model, and constitutes the universality class of these quantum systems. Once the mapping on the Luttinger model is achieved, one has an asymptotically exact solution of the 1D many-body problem. Lattice models identified as Luttinger liquids include the 1D Hubbard model off half-filling, and variants such as the t-J- or the extended Hubbard model. In addition, 1D electron-phonon systems or metals with impurities can be Luttinger liquids, as well as the edge states in the quantum Hall effect.

arXiv:cond-mat/9510014•Reports on Progress in Physics•Sep 1, 1995•1,282 citations

‘Luttinger liquid theory’ of one-dimensional quantum fluids I: Properties of the Luttinger model and their extension to the general 1D interacting spinless Fermi gas

F. D. M. Haldane

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.

Advanced series in mathematical physics•May 1, 1994•1 citation

'Luttinger liquid theory' of one-dimensional quantum fluids. I. Properties of the Luttinger model and their extension to the general 1D interacting spinless Fermi gas

F. D. M. Haldane

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.

Journal of Physics C Solid State Physics•Jul 10, 1981•2,495 citations
We discuss certain physical contents of the two-dimensional Luttinger liquid state using the spin and charge current backflow in strongly correlated electron systems. Also we attempt a description of the Luttinger liquid state in the slave boson formalism. Conventional slave boson mean field theory does not possess an important property expected of a Luttinger liquid, namely a pseudo fermi surface for holons. This arises from the bose condensation of holes. We attempt to rectify this by discussing the physics of the fermionic backflow associated with the hole motion. We argue that the fermionic backflow suppresses the Bose condensation. To understand this we introduce the notion of ‘Statistics Transfer’-the medium transfer certain statistics to the slave particle (e's). A variational wave function in which boson condensation is manifestly absent is introduced. The form of the wave function is justified by the concept of statistics transfer. The spinon and holon excitations both exhibiting pseudo fermi surfaces are constructed.
We calculate the Green's function, particle-hole susceptibility and Cooper pair susceptibility of a 2D electron gas with long range current-current interactions, using Haldane bosonization scheme. We find Luttinger Liquid properties of weakly decaying power-law tails in the spectral function and a Kohn anomaly in the 2$k\sb{F}$ particle-hole susceptibility. At finite temperature, the system exhibits more radical departure from Fermi Liquid. The specific heat was determined being linearly proportional to temperature. The strong correlations of spins and holes are demonstrated in the 2D t-J model of spin-boson and hole-fermion, through the instability against charge ordering we find from our charge susceptibility calculation of bubble and ladder diagrams. We calculate the linear-T dependence of resistivity from the hole self-energy to the second order. The excitation spectra of holon and spinon found from the self-energy calculations agree with the mean-field results to that order.
The Hubbard model in the strong coupling limit is considered in two dimensions. A bosonization method based on the extention of the Jordan-Wigner transformation to particles with spin and no double occupancy is introduced. We find that at T=0 a Fermi liquid exists and superconductivity appears. For a finite temperature and finite doping a normal state populated with vortices exists. As a result, we have a normal state with separated charge- and spin-density-wave excitations. Formally those excitations can be described with the help of the Luttinger-liquid representation. In the second part we parametrize the Fermi surface by a set of N points. Around each point we describe the Fermi surface excitations by holons and spinons and find a set of N-coupled Luttinger channels. At T=0 we have space-time tunneling of electric charges which destroys the Luttinger liquid in favor of a Fermi liquid. At T\ensuremath{\ne}0 or LT\ensuremath{\rightarrow}\ensuremath{\infty} (L is the size of the system) tunneling of electric charges might be prohibited giving rise to gapless excitations. In the last part we consider the case with a commensurate frozen flux in the ground state. As a result we find that the excitations are semions.
We review the progress in the theory of one-dimensional (ID) Fermi liquids which has occurred over the past decade. The usual Fermi liquid theory, based on a quasi-particle picture, breaks down in one dimension because of the Peierls divergence in the particle-hole bubble, producing anomalous dimensions of operators, and because of charge-spin separation. Both are related to the importance of scattering processes transferring finite momentum. A description of the low-energy properties of gapless 1D quantum systems can be based on the exactly solvable Luttinger model which incorporates these features, and whose correlation functions can be calculated. Special properties of the eigenvalue spectrum, parameterized by one renormalized velocity and one effective coupling constant per degree of freedom, fully describe the physics of this model. Other gapless 1D models share these properties in a low-energy subspace. The concept of a "Luttinger liquid" implies that their low-energy properties are described by an effective Luttinger model, and constitutes the universality class of these quantum systems. Once the mapping on the Luttinger model is achieved, one has an asymptotically exact solution of the 1D many-body problem. Lattice models identified as Luttinger liquids include the 1D Hubbard model off half-filling, and variants such as the t-J- or the extended Hubbard model. In addition, 1D electron-phonon systems or metals with impurities can be Luttinger liquids, as well as the edge states in the quantum Hall effect.
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.