Multichannel Kondo problem and some applications

We review analytical and numerical results derived from the Bethe ansatz solution of the n-channel Kondo model of arbitrary spin S as a function of temperature, external field, impurity spin S and the number of channels n. Three situations have to be distinguished: (i) If n = 2S the conduction electrons exactly compensate the impurity spin into a singlet at low temperatures, (ii) if n < 2S the impurity spin is only partially compensated (undercompensated), and (iii) if n > 2S the impurity spin is said to be overcompensated giving rise to critical behaviour. The results are discussed in the context of magnetic impurities, e.g. Fe, Cr and Tm in simple metals, the quadrupolar Kondo effect, an impurity spin embedded in the Takhtajan-Babujian Heisenberg model and electron assisted-tunnelling of an atom in a double-well potential.     

Hyperfine interaction in a quantum spin chain

From an electron spin resonance measurement on a single crystal sample of theS=1 linear chain Heisenberg antiferromagnet Ni(C₃H₁₀N₂)₂NO₂ClO₄ (NINO) containing a small amount of Cu impurity atoms, we have observed two sets of four hyperfine lines, one of which has almost three times larger field splitting than the other. The hyperfine lines are well explained as arising from the hyperfine interaction between the Cu nuclear spin andthe Cu electron spin which interact with theS=1/2 degrees of freedom induced at the Ni sites by the quantum effect. A large anisotropy in the hyperfine constant is observed andanalyzed using a ligand field theory with covalency effects.     

Solution of then-channel Kondo problem (scaling and integrability)

The exact solution of the Kondo model forn-flavours of electrons with the spin 1/2 scattered by theS-spin impurity is presented. Forn=2S=5 the model describes manganese impurities dissolved in a metal. It is shown that atn>2S the effective exchange coupling approaches a finite fixed point as the energy scale decreases. It means that atn>2S the Gell-Mann-Low function turns to zero in this point and the scaling behaviour of physical quantities is observed. The scaling behaviour, first obtained in the 1D quantum field theory, can be analyzed on the basis of the exact solution. In the casen≦2S the effective coupling becomes infinitely strong at low energies.     

Spin diffusion in anisotropic Heisenberg chains: S≥1/2

In this paper, we investigate spin diffusion in Heisenberg chains with uniaxial nearest-neighbor interactions. The approach followed is based on an analysis of the infinite-temperature longitudinal spin density and spin current correlation functions. For S=1/2, exact results are presented for the time-dependent correlation functions in the XY limit. Away from this limit, the second and fourth moments of the Fourier transform of the spin density correlation function provide information about spin dynamics for arbitrary values of the spin. The moments are used in an assessment of the accuracy of the Gaussian approximation for the spin diffusion constant for S=1/2. The general behavior of the Gaussian approximation when S>1/2 is discussed, and numerical results for the spin diffusion constant are presented for S=1/2, 1, 3/2, 2 and in the classical limit. A moment-based criterion for the boundary in reciprocal space between diffusive and non-diffusive dynamics that applies to arbitrary values of the spin is presented.     

Transport through artificial single-molecule magnets: Spin-pair state sequential tunneling and Kondo effects

The transport properties of an artificial single-molecule magnet based on a CdTe quantum dot doped with a single Mn+2 ion(S=5/2) are investigated by the non-equilibrium Green function method.We consider a minimal model where the Mn-hole exchange coupling is strongly anisotropic so that spin-flip is suppressed and the impurity spin S and a hole spin s entering the quantum dot are coupled into spin pair states with(2S+1) sublevels.In the sequential tunneling regime,the differential conductance exhibits(2S+1) possible peaks,corresponding to resonance tunneling via(2S+1) sublevels.At low temperature,Kondo physics dominates transport and(2S+1) Kondo peaks occur in the local density of states and conductance.These peaks originate from the spin-singlet state formed by the holes in the leads and on the dot via higher-order processes and are related to the parallel and antiparallel spin pair states.     

Gaussian bounds for correlations in lattice spin systems

In quite generalN-component ferromagnetic spin systems, it is proved that an arbitrary correlation function is bounded by the corresponding correlation function of a Gaussian model. The bound is useful for the analysis of high-temperature behavior of the system. Similar bounds for truncated correlation functions are also obtained for a class of single-component spin systems.     

Monte-Carlo study of correlations in quantum spin chains at non-zero temperature

Antiferromagnetic Heisenberg spin chains with various spin values (S=1/2,1,3/2,2,5/2) are studied numerically with the quantum Monte-Carlo method. Effective spin S chains are realized by ferromagnetically coupling n=2S antiferromagnetic spin chains with S=1/2. The temperature dependence of the uniform susceptibility, the staggered susceptibility, and the static structure factor peak intensity are computed down to very low temperatures, . The correlation length at each temperature is deduced from numerical measurements of the instantaneous spin-spin correlation function. At high temperatures, very good agreement with exact results for the classical spin chain is obtained independent of the value of S. For the S=2 chain which has a gap , the correlation length and the uniform susceptibility in the temperature range are well predicted by the semi-classical theory of Damle and Sachdev. Received: 23 December 1997 / Revised and Accepted: 11 March 1998     

REDOR Dephasing by Multiple Spins in the Presence of Molecular Motion

Closed-form, numerical algorithms are presented for calculating REDOR dephasing for three general cases: (i) collections of isolatedI–Sspin pairs; (ii) manySspins coupled to anIspin; and (iii) anI–Sspin pair in relative motion. For the case when more than oneSspin is dipolar coupled to anIspin, the calculation assumes that theS–Shomonuclear interaction does not affect REDOR dephasing. Full numerical simulations show that this assumption is true if theS-spin lineshapes are inhomogeneously broadened, theS-spin chemical shifts are far from rotational resonance, and a version of REDOR is used which minimizes the number ofS-spin π pulses. For the rapidly rotating –CF₃group of poly(trifluoroethyl methacrylate), the formalisms of (ii) and (iii) are combined to calculate the dephasing. The experimentally measured dephasing matches theory when the wiggling motion of the –OCH₂CF₃moiety of the polymer is taken into account.     

Non-Fermi-liquid behavior of impurity spins in the anisotropic Heisenberg chain

We consider a U(1)-invariant model consisting of the integrable anisotropic Heisenberg chain of arbitrary spin S embedding an impurity of spin S′. The impurity is assumed located on the mth link of the chain and interacting only with both neighboring sites. The coupling of the impurity to the lattice can be tuned by the impurity rapidity. The model is then integrable as a function of two continuous parameters (the anisotropy and the impurity rapidity) and two discrete variables (the spins S and S′). The thermodynamic Bethe ansatz equations are derived and used to analyze the small field and low temperature properties. Three situations have to be distinguished: (i) If S′ = S the impurity just corresponds to one more site in the chain. (ii) If S′ > S the impurity spin is only partially compensated at T = 0 and the entropy has an essential singularity at T = H = 0. (iii) If S′ < S the impurity is overcompensated, and again the entropy has an essential singularity at T = H = 0. The essential singularity gives rise to a quantum critical point and hence non-Fermi-liquid-like behavior as H and T tend to zero. While cases (i) and (iii) are analogous to the n-channel Kondo problem, case (ii) differs considerably as a consequence of critical behavior induced by the anisotropy.     

Reentrant behaviour in spin glasses

We present the phase diagram of thed-dimensional random bond Ising model as a representative system for spin glasses. We consider nearest neighbour ferromagnetic couplingsJ with concentration 1-p and impurity couplingsaJ (|a|1) with concentrationp. It is shown that for antiferromagnetic couplings, –1<a<0, the system quite generally exhibits reentrant behaviour, i.e. two phase transitions at finite temperatures, in certain ranges of the concentrationp. It is further argued that this behaviour is a quite common feature for spin glass systems characterized by competing interactions.Dedicated to B. Mühlschlegel on the occasion of his 60th birthday     

The mathematical structure of the Kondo resonance

TheT-matrix of the Nagaoka-Suhl theory for the scattering of conduction electrons from a magnetic impurity is discussed in the weak coupling limit. A law of corresponding states is established where the Kondo temperature appears as a scale factor. Some characteristic features of theT-matrix are listed which are to be used in a subsequent calculation of the spin correlation function.     

海森伯铁磁系统的总能量

对于海森伯铁磁系统,利用多体格林函数方法,在无规相近似下,并且考虑到关联函数〈S⁺S^-〉时,得到对于任意自旋S普遍适用的总能量的表达式.对于三维和二维的情况给出了计算结果.得到的总能量的数值低于没有考虑关联函数时的数值. 关键词： 海森伯模型 铁磁系统 总能量 关联函数     

Yangian symmetry in molecule {V6} and four-spin Heisenberg model

The symmetry operator Q = Y² is introduced to re-describe the Heisenberg spin triangles in the {V6} molecule, where Y stands for the Yangian operator which can be viewed as special form of Dzyaloshinsky–Moriya (DM) interaction for spin 1/2 systems. Suppose a parallelogram Heisenberg model that is comprised of four -spins commutes with Q, which mean that it possesses Yangian symmetry, we show that the ground state of the Hamiltonian H₄ for the model allows to take the total spin S = 1 by choosing some suitable exchange constants in H₄. In analogy to the molecule {V6} where the two triangles interact through Yangian operator we then give the magnetization for the theoretical molecule “{V8}” model which is comprised of two parallelograms. Following the example of molecule {V15}, we give another theoretical molecule model regarding the four -spins system with total spin S = 1 and predict the local moments to be , respectively.     

TheN/D method off the mass shell for the Klein-Gordon equation and the inversion problem

The relativistic analogon of a procedure demonstrating the link between theS-wave off-the-mass- shellN/D equations (variables: the momentum, energy and radial coordinate of a scattered particle) and the Marchenko equations of the inversion problem is presented in the static scattering. For the Klein-Gordon formalism the transition from the former type of the equations to the latter requires: a decomposition of theN/D equation quantities into the components without theE-branch points, a suitable deformation of the integration path in theN/D equations and an assumption on the regular behaviour of the off-the-mass-shellN function discontinuities.     

Exact solution for a degenerate Anderson impurity in the limit embedded into a correlated host

We consider the one-dimensional t - J model, which consists of electrons with spin S on a lattice with nearest neighbor hopping t constrained by the excluded multiple occupancy of the lattice sites and spin-exchange J between neighboring sites. The model is integrable at the supersymmetric point, J = t. Without spoiling the integrability we introduce an Anderson-like impurity of spin S (degenerate Anderson model in the limit), which interacts with the correlated conduction states of the host. The lattice model is defined by the scattering matrices via the Quantum Inverse Scattering Method. We discuss the general form of the interaction Hamiltonian between the impurity and the itinerant electrons on the lattice and explicitly construct it in the continuum limit. The discrete Bethe ansatz equations diagonalizing the host with impurity are derived, and the thermodynamic Bethe ansatz equations are obtained using the string hypothesis for arbitrary band filling as a function of temperature and external magnetic field. The properties of the impurity depend on one coupling parameter related to the Kondo exchange coupling. The impurity can localize up to one itinerant electron and has in general mixed valent properties. Groundstate properties of the impurity, such as the energy, valence, magnetic susceptibility and the specific heat coefficient, are discussed. In the integer valent limit the model reduces to a Coqblin-Schrieffer impurity. Received: 31 December 1997 / Accepted: 17 March 1998     

On the static susceptibility in the kondo problem

The dynamical susceptibility of thes-d-model is calculated in second order. It turns out, that only the impurity-impurity part of the static susceptibility contains logarithmically divergent terms. In order to obtain convergent results belowT=T _k a partial summation is carried out for this part. The final result is expressed in terms of Suhl's spin flip scattering amplitude. We find an interpolation formula for the temperature dependence of the susceptibility with complete screening of the impurity spin forS=1/2 atT=0.     

Ground state of ferromagnet with antiferromagnetic impurity

The Heisenberg ferromagnet with an antiferromagnetic impurity and arbitrary spin is considered. The method is suggested for constructing the ground state of such a system, the method using the Jacobi matrix technique. As an example, there has been investigated the ferromagnet with a simple cubic lattice and the matrix spin $\text{S =}\text{1}\text{2}$, and the impurity spin S′ = 1. The energy and wave function of the ground state are found as dependent on the system parameters.     

Thermodynamics of the spin-S antiferromagnetic Heisenberg chain

The numerical solution of the Bethe ansatz equations of an integrableSU (2)-invariant generalization of the spin-S antiferromagnetic Heisenberg chain in zero magnetic field is presented. The thermodynamics is obtained numerically. The temperature dependence of the entropy, specific heat and susceptibility is presented forS5/2. The results are compared to those of then-channel Kondo problem with a spin-S impurity withn=2S.     

Evolution of the entropy of stationary states in selforganization processes in the control parameter space

The behaviour of entropy (Shannon-information) and renormalized entropy (based on theS-theorem [3]) is investigated for systems with an exponential stationary probability distribution function (1). Analytical results for the derivatives with respect to the control parameters are derived. One class of systems (3) is separated for which the renormalized entropy is a monotonously decreasing function of the control parameters.