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Europhysics Letters (EPL)

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

Debanand Sa

Published May 1, 1998• 3 citations
Publisher

Abstract

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.

DOI
10.1209/epl/i1998-00244-6

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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.
The effect of static impurities in a two-dimensional quantum antiferromagnet has been studied. Creation of a vacancy in an antiferromagnetic lattice yields an impurity Hamiltonian whose x-y part maps to single impurity Anderson model whereas the z-part becomes the X-ray singularity problem. The model is solved where one obtains a bound state giving rise to δ-function density of states. The z-part of the interaction makes this peak asymmetric which follows a power law. It has been argued that the bound state corresponds to a local moment in the system giving rise to Curie-like contribution to the susceptibility. The implications of the present model in the substitutional Zn doped high-T c oxides have been discussed.
An exactly solvable one-dimensional Hubbard model with a single Anderson impurity embedded at the boundary is constructed in the framework of the quantum inverse scattering method. The model is solved exactly by the nested Bethe ansatz method. We identify the boundary bound states and determine the ground state phase diagram. By analyzing the impurity contributions to the magnetization density and magnetic susceptibility, we demonstrate that a local moment is formed at the impurity site and is screened by the host electrons, consistent with Kondo physics.
We study, using numerical exact diagonalisation, some static and dynamical properties of a single impurity substituted into a one-dimensional repulsive Hubbard chain. A systematic scan of the parameter-space reveals a rich magnetic phase diagram. Interactions on the lattice stabilize the local moment phase of the impurity. A scalar impurity is seen to induce local moments on the neighbouring sites near Half Filling. Static spin and charge correlation functions reflect a non-Fermi liquid character of the ground state in the presence of a scalar impurity.
We introduce the notion of an impurity susceptibility as a measure of the effect of disorder on the properties of interacting many-particle systems. If finite, the impurity susceptibility gives the lowest-order correction to a given physical observable in the presence of disorder. If divergent, it signals that arbitrarily weak disorder leads to a qualitatively different physical behavior. Using a quantum Monte Carlo technique, impurity susceptibilities for various properties of the one-dimensional Hubbard model are calculated. Two types of disorder are considered; random hopping matrix elements and random potentials. For the local magnetic moment and the kinetic energy the impurity susceptibilities are finite. The impurity susceptibility of the q=2kF{\mathit{k}}_{\mathit{F}}kF​ spin response is divergent for both types of disorder, indicating a quenching of the T\ensuremath{\rightarrow}0 divergence of this quantity. The susceptibility of the q=0 spin response to random hopping diverges at half filling, as a consequence of a divergent magnetic susceptibility in the presence of this type of disorder. We also find large, possibly divergent, impurity susceptibilities for the q=2kF{\mathit{k}}_{\mathit{F}}kF​ and 4kF{\mathit{k}}_{\mathit{F}}kF​ charge-density responses.
A Green's-function method is used to obtain the exact expression for the local susceptibility of the impure spin-1/2 XY chain at zero temperature. The presence of the impurity (or boundary) affects the singularity of the magnetic field dependence of the local susceptibility. The corresponding critical exponent changes from -1/2 to +1/2 at an arbitrary distance from the impurity site. In contrast with the transverse Ising model, the critical exponent is independent of the perturbation strength. This phenomenon is related to the spatial oscillations of the local density of states in the nonideal XY chain. It is also shown that experimental investigation of the field dependence of the finite-temperature macroscopic susceptibility of the one-dimensional XY-like system (such as Cs2{\mathrm{Cs}}_{2}Cs2​CoCl4{\mathrm{CoCl}}_{4}CoCl4​) may reveal the formation of the localized states associated with impurities.
We investigate magnetic properties induced by a spinless impurity in strongly correlated electron systems, i.e., the Hubbard model in spatial dimension D=1,2,D=1,2,D=1,2, and 3.3.3. For the one-dimensional (1D) system exploiting the Bethe ansatz exact solution we find that the spin susceptibility and the local density of states in the vicinity of a spinless impurity show divergent behaviors. The results imply that the induced local moment is not completely quenched at any finite temperatures. On the other hand, the spin lattice relaxation rate obtained by bosonization and boundary conformal field theory satisfies a relation analogous to the Korringa law, ${1/T}_{1}T\ensuremath{\sim}{\ensuremath{\chi}}^{2}.$ In the 2D and 3D systems, the analysis based upon the antiferromagnetically correlated Fermi liquid theory reveals that the antiferromagnetic spin fluctuation developed in the bulk is much suppressed in the vicinity of a spinless impurity, and thus magnetic properties are governed by the induced local moment, which leads to the Korringa law of 1/T1.{1/T}_{1}.1/T1​.