The anisotropic multichannel spin- $\mathsf{S}$ Kondo model: Calculation of scales from a novel exact solutionThe anisotropic multichannel spin-$\mathsf{S}$ Kondo model: Calculation of scales from a novel exact solution

Michael Bortz, A. Klümper

arXiv:cond-mat/0409755The European Physical Journal BJul 1, 20046 citations

Reflection Positivity in Spin Space for the Heisenberg Model, the Kondo Hamiltonian and the Kondo Lattice

Takashi Yanagisawa

In this article we discuss the reflection positivity in spin space for the Heisenberg model and the Kondo Hamiltonian. We show that the ground state is unique for J ≠0 where J is the strength of the exchange interaction in the Heisenberg model or the exchange coupling between the localized spins and conduction electrons in the Kondo model. We introduce the Coulomb interaction U >0 between the conduction lectrons for the Kondo Hamiltonian to show the uniqueness of the ground state. We write the Hamiltonian in terms of fermions to express the exchange interactions and impose constraints. We employ the Lagrange-multiplier method to deal with the constraints in this work.In this article we discuss the reflection positivity in spin space for the Heisenberg model and the Kondo Hamiltonian. We show that the ground state is unique for J ≠0 where J is the strength of the exchange interaction in the Heisenberg model or the exchange coupling between the localized spins and conduction electrons in the Kondo model. We introduce the Coulomb interaction U >0 between the conduction lectrons for the Kondo Hamiltonian to show the uniqueness of the ground state. We write the Hamiltonian in terms of fermions to express the exchange interactions and impose constraints. We employ the Lagrange-multiplier method to deal with the constraints in this work.

Journal of the Physical Society of JapanJul 15, 19961 citation

Spin-Spin Correlations in the 2-Impurity Kondo Problem

Leena Chandran, H. R. Krishnamurthy, Ciriyam Jayaprakash

Springer eBooksJan 1, 19870 citations

On the pseudo-fermion representation of the Kondo Hamiltonian

Hans C. Fogedby

Physics Letters ASep 1, 19723 citations

On the completeness of Wiegmann's solution to the Kondo problem

C C Lai, WU YONG-SHI

The recent solution by Wiegmann of the Kondo problem is re-examined to some detail. Special attention is paid to the problem of completeness which is essential to thermodynamic calculations. After obtaining the most general solution to the Kondo Hamiltonian, it is proved rigorously that solutions obtained with the Bethe ansatz do form a complete set. It is also shown that the Wiegmann solutions, being a subset of the Bethe solutions, are not complete although they are obtainable from the latter via some physical arguments.The recent solution by Wiegmann of the Kondo problem is re-examined to some detail. Special attention is paid to the problem of completeness which is essential to thermodynamic calculations. After obtaining the most general solution to the Kondo Hamiltonian, it is proved rigorously that solutions obtained with the Bethe ansatz do form a complete set. It is also shown that the Wiegmann solutions, being a subset of the Bethe solutions, are not complete although they are obtainable from the latter via some physical arguments.

Journal of Physics C Solid State PhysicsOct 30, 19815 citations

Monte Carlo simulation of the ‘‘Kondo necklace’’

Richard T. Scalettar, Douglas J. Scalapino, Robert L. Sugar

The projector Monte Carlo method and finite-size scaling are applied to the solution of the ground-state properties of the ``Kondo necklace'' Hamiltonian. The energy and various spin-spin correlation functions are calculated for chains up to 16 sites in length. Correlations between the spins on different sites are evaluated, and the nature of the ground-state phase as a function of the ratio of the exchange coupling J to the bandwidth W is examined. Evaluation of the correlation function 〈S\ensuremath{\rightarrow}(i)\ensuremath{\cdot}\ensuremath{\tau}\ensuremath{\rightarrow}(i)〉 shows that as the coupling between the localized S spins and the \ensuremath{\tau} spin chain increases, the system becomes composed of independent singlets on each site. Contrary to both mean-field and various approximate renormalization-group calculations, we find that our results are consistent with an absence of magnetic order as soon as J is different from 0.The projector Monte Carlo method and finite-size scaling are applied to the solution of the ground-state properties of the ``Kondo necklace'' Hamiltonian. The energy and various spin-spin correlation functions are calculated for chains up to 16 sites in length. Correlations between the spins on different sites are evaluated, and the nature of the ground-state phase as a function of the ratio of the exchange coupling J to the bandwidth W is examined. Evaluation of the correlation function 〈S\ensuremath{\rightarrow}(i)\ensuremath{\cdot}\ensuremath{\tau}\ensuremath{\rightarrow}(i)〉 shows that as the coupling between the localized S spins and the \ensuremath{\tau} spin chain increases, the system becomes composed of independent singlets on each site. Contrary to both mean-field and various approximate renormalization-group calculations, we find that our results are consistent with an absence of magnetic order as soon as J is different from 0.

Physical review. B, Condensed matterJun 1, 198545 citations

The anisotropic multichannel spin-

\mathsf{S}

Kondo model: Calculation of scales from a novel exact solution