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physica status solidi (b)

Oscillations of Local Magnetization in the Non‐Ideal Antiferromagnetic Chain

Gennady Sh. Gildenblat

Published Dec 1, 1983• 3 citations
Publisher

Abstract

Abstract A Green's function technique is used to obtain the exact form of the Friedel type oscillations of local magnetization in the spin 1/2, XY antiferromagnetic chain induced by the presence of a boundary or impurity. It is shown that, in addition to the amplitude, the functional form of the oscillations is determined by the strength of the perturbation caused by the impurity and intensity of the external magnetic field. Comparison is made with the earlier perturbation theory treatment in the free‐fermion approximation.

DOI
10.1002/pssb.2221200208

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Journal of Computational Chemistry•Dec 1, 1982•32 citations
Abstract A Green's function technique is used to obtain the exact form of the Friedel type oscillations of local magnetization in the spin 1/2, XY antiferromagnetic chain induced by the presence of a boundary or impurity. It is shown that, in addition to the amplitude, the functional form of the oscillations is determined by the strength of the perturbation caused by the impurity and intensity of the external magnetic field. Comparison is made with the earlier perturbation theory treatment in the free‐fermion approximation.
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.
Abstract The interplay between disorder and interaction, especially near metal insulator transitions, is a long‐standing question. We investigate in detail single impurities, in particular, the Friedel oscillations induced by them. We study the decay of the Friedel oscillations in the one‐dimensional Heisenberg and Hubbard model analytically using the bosonization technique and numerically using the density matrix renormalization group treatment (DMRG). For the Heisenberg chain, we confirm the predictions of conformal field theory and bosonization for small interaction, but near phase transitions deviations are found in form of vanishing or additional oscillations. For the Hubbard chain, we study the oscillations – in the density as well as in the magnetization – in the spin‐gap, charge‐gap, and Luttinger liquid phase. We find an exponential decay or a very slow algebraic decay of the oscillations in the gapped phases. In the Luttinger liquid phase, we concentrate on the question of logarithmic corrections (which occur also in the isotropic Heisenberg antiferromagnet). Differences in the behavior near a boundary compared to an impurity are pointed out. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Hartree-Fock equations for the impure spin-\textonehalf{} Ising-Heisenberg chain are derived by using the Green-function technique in the pseudofermion representation. The self-consistency equations for the ideal spin-\textonehalf{} anisotropic Heisenberg antiferromagnet can be recovered as a specific case of the general formalism developed in the present work. In the case of the nonideal XXZ\mathrm{XXZ}XXZ chain, a numerical solution of the self-consistency equations is used to describe the Friedel-type boundary on impurity-induced oscillations of the local magnetization considered previously in the spin-\textonehalf{}XY\mathrm{XY}XY model.
We derive compact multiple integral formulae for several physical spin correlation functions in the semi-infinite XXZ chain with a longitudinal boundary magnetic field. Our formulae follow from several effective resummations of the multiple integral representation for the elementary blocks obtained in our previous paper (I). In the free fermion point we compute the local magnetization as well as the density of energy profiles. These quantities, in addition to their bulk behavior, exhibit Friedel-type oscillations induced by the boundary; their amplitudes depend on the boundary magnetic field and decay algebraically in terms of the distance to the boundary.
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.