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

physica status solidi (b)

The Local and Quasi‐Local Impurity States in the Finite One‐Dimensional Hubbard Model

Ilia D. Mikhailov, I. Yu. Shelestina

Published Sep 1, 1974• 0 citations
Publisher

Abstract

Abstract An analytic expression for the Green's function of the ground state of the finite one‐dimensional Hubbard model and the density of the electronic states on the sites are obtained. It is shown that the introduction of a local perturbation can cause the formation of quasilocalized levels which may transform into localized states when the pertubation reaches some critical value.

DOI
10.1002/pssb.2220650136

Related papers

Quasi‐one‐dimensional systems and localized defects: Some results of the Green's matrix formalism

Max Seel, Giuseppe Del Re, Janos J. Ladik

Abstract The application of the self‐consistent field (SCF) local‐impurity formalism to quasi‐one‐dimensional systems is discussed. We describe a general procedure for an accurate numerical determination of the Green's function matrix elements of the unperturbed system. An application to a local impurity in a model chain with two orbitals per unit cell is reported. The changes in the charge‐bond‐order matrix and in local and total density of states due to the impurity are discussed with special emphasis on the changes at the critical points (van Hove singularities) at the band edges. The Green's matrix approach is used to reexamine long‐range Friedel oscillations caused by an impurity in a strictly one‐dimensional metal. The extent of the long‐range tail of the perturbed charge density is in an inverse relation to the localization length of the impurity state: the stronger the perturbation the more localized is the bound state and the more extended are the oscillations in the charge distribution. The results for the model chain with two orbitals per unit cell indicate that the impurity‐induced change in charge distribution may be locally screened by redistribution of the population of the on‐site orbitals, therefore damping possible oscillations and leading to a faster decay than in strictly one‐dimensional systems.

Journal of Computational Chemistry•Dec 1, 1982•32 citations

Ground state of the one-dimensional half-filled Hubbard model

N. I. Chashchin

We investigate the ground state (T = 0 K) of the one-dimensional symmetrical (n = 1) Hubbard model formalized in terms of the system of integral equations, which we previously obtained using the method of the generating functional of Green’s functions with the subsequent Legendre transformation. In a wide range of variations in the parameter of Coulomb interaction U, the following characteristics of the system have been calculated: the electron density of states, the electron band spectrum, the number of doubly occupied lattice sites, the localized magnetic moment, the correlator of the square of the longitudinal component of spin at a site,<S Z 2>, and the internal energy of the system. It has been shown that, for all U > 0, the model yields two solutions, i.e., an antiferromagnetic insulator and a paramagnetic insulator, in which there are no single-electron quasi-particles at the Fermi level. The energy of the paramagnetic solution in the region of U < 1.1 is considerably less than that of the antiferromagnetic solution for the case of U > 1.1, we have the opposite situation.

The Physics of Metals and Metallography•Jul 1, 2016•0 citations

LOCAL PAIRING IN THE ATTRACTIVE HUBBARD MODEL

S. Di Matteo, Mancini, Marra

this article we shall consider the case of the Hubbard model with on-site attraction. In Section 2 we derive the explicit expression for the Green's function, in the static approximation. In Section 3 we present some results for the double occupancy and the spin magnetic susceptibility for the case of half filling. By analytic method we can show that at zero temperature the system exhibits a phase transition to a pair state, where all the electrons are locally paired in a singlet state; the critical value U c for the interaction potential at which the phase transition occurs is equal to U c =-8t, 8t being the band width.

Condensed Matter Physics•Jan 1, 1996•3 citations

WEAK-COUPLING TREATMENT OF THE HUBBARD-MODEL IN THE HIGH-DIMENSIONAL AND LOW-DIMENSIONAL SYSTEMS

Kyuhwe Kang, Byung Il Min

Employing the equation of motion method for the Green's function, we have obtained the self-energy for the Hubbard model in the weak correlation limit up to the 2nd order in U, the on-site interaction strength. The quasi-particle spectral density of states is determined numerically, using the local approximation which is known to be exact for the infinite dimensional Hubbard model. Further, assuming a linear dispersion for the bare electronic spectra for the 1D Hubbard model, we have evaluated analytically the imaginary part of the self-energy, Im Sigma, near the Fermi energy (E(F)) and the renormalization coefficient at E(F), Z(F). It is found that the 1D Hubbard model system exhibits a non-Fermi liquid behavior within the 2nd order perturbational treatment.

•Jan 1, 1995•0 citations

Pertubation theory about self-consistent field solution in one-dimensional Hubbard model

Kocharian AN; Yang C; Chiang YL

[[abstract]]The accurate analytical and numerical calculations of the electronic band structure and ground state properties of strongly correlated electrons within the Hubbard model are performed by constructing convergent perturbation theory for general interaction strength and electron concentration. We test the developed perturbation approach about mean field solution in the extreme conditions of one dimensionality for entire parameter space of electron interaction U/t and electron concentration n. The many-body perturbation formalism up two second order about the generalized self-consistent field (GSCF) Hamiltonian goes beyond the range of applicability of standard perturbation theory by incorporating systematically the effect of the random-phase-type perturbation techniques and controlled expansion of the energy functional for general U/t and n. The second order perturbation correction vanishes at small and large U/t limit and performed calculations of the ground state energy show a next to the perfect numerical agreement with the Bethe-ansatz results.

•Jan 1, 2003•0 citations

Formation of local moment near a static vacancy in the one-dimensional large- U Hubbard model

Debanand Sa

The effect of non-magnetic impurities in the one-dimensional large- U Hubbard model has been studied. For a single non-magnetic scatterer, it is shown that a bound state is obtained which is due to the singular behaviour of the T -matrix. It has been argued that the bound state which yields a δ-function density of states might correspond to local moment in the system giving rise to Curie-like contribution to the susceptibility. The spatial dependence of the impurity state wave function is shown to follow an algebraic decay. Its possible relevance to some recently discovered one-dimensional antiferromagnets has been discussed.

Europhysics Letters (EPL)•May 1, 1998•3 citations
Abstract An analytic expression for the Green's function of the ground state of the finite one‐dimensional Hubbard model and the density of the electronic states on the sites are obtained. It is shown that the introduction of a local perturbation can cause the formation of quasilocalized levels which may transform into localized states when the pertubation reaches some critical value.
Abstract The application of the self‐consistent field (SCF) local‐impurity formalism to quasi‐one‐dimensional systems is discussed. We describe a general procedure for an accurate numerical determination of the Green's function matrix elements of the unperturbed system. An application to a local impurity in a model chain with two orbitals per unit cell is reported. The changes in the charge‐bond‐order matrix and in local and total density of states due to the impurity are discussed with special emphasis on the changes at the critical points (van Hove singularities) at the band edges. The Green's matrix approach is used to reexamine long‐range Friedel oscillations caused by an impurity in a strictly one‐dimensional metal. The extent of the long‐range tail of the perturbed charge density is in an inverse relation to the localization length of the impurity state: the stronger the perturbation the more localized is the bound state and the more extended are the oscillations in the charge distribution. The results for the model chain with two orbitals per unit cell indicate that the impurity‐induced change in charge distribution may be locally screened by redistribution of the population of the on‐site orbitals, therefore damping possible oscillations and leading to a faster decay than in strictly one‐dimensional systems.
We investigate the ground state (T = 0 K) of the one-dimensional symmetrical (n = 1) Hubbard model formalized in terms of the system of integral equations, which we previously obtained using the method of the generating functional of Green’s functions with the subsequent Legendre transformation. In a wide range of variations in the parameter of Coulomb interaction U, the following characteristics of the system have been calculated: the electron density of states, the electron band spectrum, the number of doubly occupied lattice sites, the localized magnetic moment, the correlator of the square of the longitudinal component of spin at a site,<S Z 2>, and the internal energy of the system. It has been shown that, for all U > 0, the model yields two solutions, i.e., an antiferromagnetic insulator and a paramagnetic insulator, in which there are no single-electron quasi-particles at the Fermi level. The energy of the paramagnetic solution in the region of U < 1.1 is considerably less than that of the antiferromagnetic solution for the case of U > 1.1, we have the opposite situation.
this article we shall consider the case of the Hubbard model with on-site attraction. In Section 2 we derive the explicit expression for the Green's function, in the static approximation. In Section 3 we present some results for the double occupancy and the spin magnetic susceptibility for the case of half filling. By analytic method we can show that at zero temperature the system exhibits a phase transition to a pair state, where all the electrons are locally paired in a singlet state; the critical value U c for the interaction potential at which the phase transition occurs is equal to U c =-8t, 8t being the band width.
Employing the equation of motion method for the Green's function, we have obtained the self-energy for the Hubbard model in the weak correlation limit up to the 2nd order in U, the on-site interaction strength. The quasi-particle spectral density of states is determined numerically, using the local approximation which is known to be exact for the infinite dimensional Hubbard model. Further, assuming a linear dispersion for the bare electronic spectra for the 1D Hubbard model, we have evaluated analytically the imaginary part of the self-energy, Im Sigma, near the Fermi energy (E(F)) and the renormalization coefficient at E(F), Z(F). It is found that the 1D Hubbard model system exhibits a non-Fermi liquid behavior within the 2nd order perturbational treatment.
[[abstract]]The accurate analytical and numerical calculations of the electronic band structure and ground state properties of strongly correlated electrons within the Hubbard model are performed by constructing convergent perturbation theory for general interaction strength and electron concentration. We test the developed perturbation approach about mean field solution in the extreme conditions of one dimensionality for entire parameter space of electron interaction U/t and electron concentration n. The many-body perturbation formalism up two second order about the generalized self-consistent field (GSCF) Hamiltonian goes beyond the range of applicability of standard perturbation theory by incorporating systematically the effect of the random-phase-type perturbation techniques and controlled expansion of the energy functional for general U/t and n. The second order perturbation correction vanishes at small and large U/t limit and performed calculations of the ground state energy show a next to the perfect numerical agreement with the Bethe-ansatz results.
The effect of non-magnetic impurities in the one-dimensional large- U Hubbard model has been studied. For a single non-magnetic scatterer, it is shown that a bound state is obtained which is due to the singular behaviour of the T -matrix. It has been argued that the bound state which yields a δ-function density of states might correspond to local moment in the system giving rise to Curie-like contribution to the susceptibility. The spatial dependence of the impurity state wave function is shown to follow an algebraic decay. Its possible relevance to some recently discovered one-dimensional antiferromagnets has been discussed.