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

arXiv:cond-mat/0205147 · Physical review. B, Condensed matter

Strongly interacting Luttinger liquid and superconductivity in an exactly solvable model

Igor N. Karnaukhov, Alexander A. Ovchinnikov

Published Sep 25, 2002• 5 citations
arXivHTMLPDF

Abstract

A family of exactly solvable one-dimensional models with a hard-core repulsive potential is solved by the Bethe ansatz for an arbitrary hard-core radius. The exact ground state phase diagrams in a plane ``electron-density--on-site interaction'' have been studied for several values of a hard-core radius. It is shown that strongly interacting Luttinger liquid can be realized in superconducting state at a high electron density and high value of repulsive on-site Coulomb interaction.

DOI
10.1103/physrevb.66.104518

Related papers

From the integrable one-parameter Lai-Sutherland model to a strongly interacting Luttinger liquid state

Igor N. Karnaukhov

One parameter family of the Lai-Sutherland models with hard-core repulsive potential is formulated and solved by the Bethe ansatz method in one dimension for an arbitrary core radius (Δ + 1)/2. The ground-state Bethe ansatz equations are analysed and solved numerically for an arbitrary electron density, several values of color components, and the core radius. The ground-state energy, the Fermi velocity, and the critical exponents describing the asymptotic behavior of the correlation functions at long distances have been calculated numerically for an arbitrary density of electrons. In contrast to the integrable models studied previously, the long-distance behavior is described by a strongly interacting Luttinger liquid state. This state is characterized by a large value of the critical exponent Θ for the momentum distribution function (Θ > 1) and realized at a high electron density region n > n c (Θ( n c ) = 1).

Europhysics Letters (EPL)•Dec 1, 2000•4 citations

Strongly interacting Luttinger-liquid state in the integrable model of spinless fermions

Igor N. Karnaukhov

A family of spinless fermion models with a hard core potential is formulated and solved by the Bethe ansatz method in one dimension for an arbitrary core radius. The Hamiltonian has two levels of strong interaction: the repulsive hard core potential and the kinetic energy with hopping integrals, values of which depend on the configuration of the particles. The Fermi velocity and the critical exponents describing the asymptotic behavior of the correlation functions at long distances have been calculated numerically for an arbitrary density of electrons and hard core radius. We discuss the effect of the hard core potential. The hard core potential defines an anomalous behavior of the critical exponent \ensuremath{\Theta} of the momentum distribution function. In the high-electron-density region the long-distance behavior is described by a strongly interacting Luttinger-liquid state with \ensuremath{\Theta}>1 and the residual Fermi surface disappears.

Physical review. B, Condensed matter•Jan 3, 2001•3 citations

One-dimensional strongly interacting Luttinger liquid of lattice spinless fermions

I. N Karnaukhov, A. A Ovchinnikov

We consider the spinless fermion model with hard-core repulsive potential between particles extended on a few lattice sites δ. The Luttinger-liquid behavior is studied for different values of a hard-core radius. We derive a critical exponent Θ of the one-particle correlation function ⟨ c i † c j ⟩ for an arbitrary electron density and coupling constant. Our results show that at high density the behavior of fermions can be described as a strongly interacting Luttinger liquid with Θ > 1. As a result, the residual Fermi surface disappears.

arXiv:cond-mat/0110289•Europhysics Letters (EPL)•Feb 1, 2002•19 citations

One-dimensional strongly interacting Luttinger liquid of lattice spinless fermions

Igor N. Karnaukhov, Alexander A. Ovchinnikov

We consider the spinless fermion model with hard-core repulsive potential between particles extended on a few lattice sites delta. The Luttinger-liquid behavior is studied for different values of a hard-core radius. We derive a critical exponent Theta of the one-particle correlation function [c(i)(dagger)c(j)] for an arbitrary electron density and coupling constant. Our results show that at high density the behavior of fermions can be described as a strongly interacting Luttinger liquid with Phi > 1. As a result, the residual Fermi surface disappears.

•Jan 1, 2002•6 citations

Luttinger Liquid State with Effective Attractive Hare-Core Interaction

Igor N. Karnaukhov

An exact solvable 'zig-zag' ladder model of degenerated spinless fermions is proposed and solved exactly by the means of the Bethe ansatz. An effective attractive hard-core interaction and direct Coulomb repulsion of fermions on the nearest-neighbor sites of different chains induce a new phase state of the ladder. We give a detailed analysis of the exact phase diagram at zero temperature, that is characterized by two phases at the filling exceeding 2/3: itinerant and 'frozen' fermions, for which two different species reside in spatially separate regions. The critical exponents describing asymptotic behavior of the correlation functions are calculated using the Bethe ansatz and conformal field theory. It is shown also, that the density of the magnetization of the corresponding zig-zag spin-1/2 ladder has a jump equal to 1/3 at the magnetic field equal to zero.

arXiv:0708.1375•Aug 10, 2007•0 citations

Strongly interacting Luttinger liquid - exact solution of a generalizedt-Jmodel in one dimension

Igor N. Karnaukhov, Natan Andrei

Luttinger liquids are characterized by the critical exponent Θ of the momentum distribution around the Fermi momentum k F . Typically Θ⩽1/2, signalling a singularity characterizing a residual Fermi surface. Results of photoemission experiments can be interpreted in terms strongly interacting Luttinger liquids with Θ⩾1 with the residual Fermi surface disappearing. We construct integrable models with such behaviour - models given by the SU(ν) t - J interaction with a hard-core repulsive potential between electrons at distances less than or equal to Δ. The models exhibit both weakly and strongly interacting Luttinger behaviours with Θ varying continuously in the range 0⩽Θ⩽½(1 + Δ-1/[ν(1 + Δ)]) 2 depending on the electron density. In the extreme high-density limit the model exhibits a Mott-Hubbard gap and reduces to an isotropic Heisenberg chain with a new spacing parameter Δ + 1.

Journal of Physics Condensed Matter•Oct 19, 2001•4 citations
A family of exactly solvable one-dimensional models with a hard-core repulsive potential is solved by the Bethe ansatz for an arbitrary hard-core radius. The exact ground state phase diagrams in a plane ``electron-density--on-site interaction'' have been studied for several values of a hard-core radius. It is shown that strongly interacting Luttinger liquid can be realized in superconducting state at a high electron density and high value of repulsive on-site Coulomb interaction.
One parameter family of the Lai-Sutherland models with hard-core repulsive potential is formulated and solved by the Bethe ansatz method in one dimension for an arbitrary core radius (Δ + 1)/2. The ground-state Bethe ansatz equations are analysed and solved numerically for an arbitrary electron density, several values of color components, and the core radius. The ground-state energy, the Fermi velocity, and the critical exponents describing the asymptotic behavior of the correlation functions at long distances have been calculated numerically for an arbitrary density of electrons. In contrast to the integrable models studied previously, the long-distance behavior is described by a strongly interacting Luttinger liquid state. This state is characterized by a large value of the critical exponent Θ for the momentum distribution function (Θ > 1) and realized at a high electron density region n > n c (Θ( n c ) = 1).
A family of spinless fermion models with a hard core potential is formulated and solved by the Bethe ansatz method in one dimension for an arbitrary core radius. The Hamiltonian has two levels of strong interaction: the repulsive hard core potential and the kinetic energy with hopping integrals, values of which depend on the configuration of the particles. The Fermi velocity and the critical exponents describing the asymptotic behavior of the correlation functions at long distances have been calculated numerically for an arbitrary density of electrons and hard core radius. We discuss the effect of the hard core potential. The hard core potential defines an anomalous behavior of the critical exponent \ensuremath{\Theta} of the momentum distribution function. In the high-electron-density region the long-distance behavior is described by a strongly interacting Luttinger-liquid state with \ensuremath{\Theta}>1 and the residual Fermi surface disappears.
We consider the spinless fermion model with hard-core repulsive potential between particles extended on a few lattice sites δ. The Luttinger-liquid behavior is studied for different values of a hard-core radius. We derive a critical exponent Θ of the one-particle correlation function ⟨ c i † c j ⟩ for an arbitrary electron density and coupling constant. Our results show that at high density the behavior of fermions can be described as a strongly interacting Luttinger liquid with Θ > 1. As a result, the residual Fermi surface disappears.
We consider the spinless fermion model with hard-core repulsive potential between particles extended on a few lattice sites delta. The Luttinger-liquid behavior is studied for different values of a hard-core radius. We derive a critical exponent Theta of the one-particle correlation function [c(i)(dagger)c(j)] for an arbitrary electron density and coupling constant. Our results show that at high density the behavior of fermions can be described as a strongly interacting Luttinger liquid with Phi > 1. As a result, the residual Fermi surface disappears.
An exact solvable 'zig-zag' ladder model of degenerated spinless fermions is proposed and solved exactly by the means of the Bethe ansatz. An effective attractive hard-core interaction and direct Coulomb repulsion of fermions on the nearest-neighbor sites of different chains induce a new phase state of the ladder. We give a detailed analysis of the exact phase diagram at zero temperature, that is characterized by two phases at the filling exceeding 2/3: itinerant and 'frozen' fermions, for which two different species reside in spatially separate regions. The critical exponents describing asymptotic behavior of the correlation functions are calculated using the Bethe ansatz and conformal field theory. It is shown also, that the density of the magnetization of the corresponding zig-zag spin-1/2 ladder has a jump equal to 1/3 at the magnetic field equal to zero.
Luttinger liquids are characterized by the critical exponent Θ of the momentum distribution around the Fermi momentum k F . Typically Θ⩽1/2, signalling a singularity characterizing a residual Fermi surface. Results of photoemission experiments can be interpreted in terms strongly interacting Luttinger liquids with Θ⩾1 with the residual Fermi surface disappearing. We construct integrable models with such behaviour - models given by the SU(ν) t - J interaction with a hard-core repulsive potential between electrons at distances less than or equal to Δ. The models exhibit both weakly and strongly interacting Luttinger behaviours with Θ varying continuously in the range 0⩽Θ⩽½(1 + Δ-1/[ν(1 + Δ)]) 2 depending on the electron density. In the extreme high-density limit the model exhibits a Mott-Hubbard gap and reduces to an isotropic Heisenberg chain with a new spacing parameter Δ + 1.