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Journal de Physique IV (Proceedings)

Integrable fermion model with hopping integrals for many particle configurations

Igor N. Karnaukhov

Published Mar 1, 2000• 0 citations
Publisher

Abstract

One parametric one-dimensional spinless fermion models is formulated and solved exactly by the Bethe ansatz method. The Hamiltonian contains the kinetic terms describing nearest-neighbor hopping of electrons with different hopping integrals for many particle configurations. The Luttinger liquid behavior is studied for the case repulsion effective interactions. The ground state energy, the critical exponent, describing the asymptotic behavior of the density-density correlation function at long distances, the Fermi velocity have been calculated numerically for an arbitrary density of electrons. The model displays the condensation of particles in the case of the attractive interaction.

DOI
10.1051/jp4:2000570

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One parametric one-dimensional spinless fermion models is formulated and solved exactly by the Bethe ansatz method. The Hamiltonian contains the kinetic terms describing nearest-neighbor hopping of electrons with different hopping integrals for many particle configurations. The Luttinger liquid behavior is studied for the case repulsion effective interactions. The ground state energy, the critical exponent, describing the asymptotic behavior of the density-density correlation function at long distances, the Fermi velocity have been calculated numerically for an arbitrary density of electrons. The model displays the condensation of particles in the case of the attractive interaction.
One parametric one-dimensional spinless fermion model is formulated and solved exactly by the Bethe ansatz method. The Hamiltonian contains the kinetic terms describing nearest-neighbor hopping of electrons with different hopping integrals for many-particle configurations. The Luttinger liquid behavior is studied for the case repulsion effective interaction. The ground-state energy, the critical exponent, describing the asymptotic behavior of the density-density correlation function at long distances, the Fermi velocity have been calculated numerically for an arbitrary density of electrons. The model displays the condensation of particles in the case of the attractive interaction.
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.
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 new supersymmetric model for electrons with generalized hopping terms and Hubbard interaction on a one-dimensional lattice is solved by means of the Bethe ansatz. We investigate the phase diagram of this model by studying the ground state and excitations of the model as a function of the interaction parameter, electronic density and magnetization. Using arguments from conformal field theory we can study the critical exponents describing the asymptotic behaviour of correlation functions at long distances.
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.