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Chinese Physics Letters

Mapping the Spinless Fermion-Boson Model onto a Luttinger Liquid Model

Yupeng Wang, Fu-ke Pu

Published Nov 1, 1996• 1 citation
Publisher

Abstract

The spinless fermion-boson model in one-dimension is studied via the Bethe ansatz method. The eigenstates of the model Hamiltonian are established. Some long distance correlation functions are calculated based on the prediction of the conformal field theory. It is shown that the low energy physics of the present model is equivalent to that of a Luttinger liquid model.

DOI
10.1088/0256-307x/13/11/001

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The spinless fermion-boson model in one-dimension is studied via the Bethe ansatz method. The eigenstates of the model Hamiltonian are established. Some long distance correlation functions are calculated based on the prediction of the conformal field theory. It is shown that the low energy physics of the present model is equivalent to that of a Luttinger liquid model.
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 discuss the technique of bosonization for studying systems of interacting fermions in one dimension. After briefly reviewing the low-energy properties of Fermi and Luttinger liquids, we present some of the relations between bosonic and fermionic operators in one dimension. We use these relations to calculate the correlation functions and the renormalization group properties of various operators for a system of spinless fermions. We then apply the methods of bosonization to study the Heisenberg antiferromagnetic spin 1/2 chain, the Hubbard model in one dimension, and transport in clean quantum wires and in the presence of isolated impurities.
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.
We discuss the technique of bosonization for studying systems of interacting fermions in one dimension. After briefly reviewing the low-energy properties of Fermi and Luttinger liquids, we present some of the relations between bosonic and fermionic operators in one dimension. We use these relations to calculate the correlation functions and the renormalization group properties of various operators for a system of spinless fermions. We then apply the methods of bosonization to study the Heisenberg antiferromagnetic spin 1/2 chain, the Hubbard model in one dimension and transport in clean quantum wires and in the presence of isolated impurities.
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.