In this paper, we discuss the effect of the arbitrary spin impurities to the spin-1/2 and spin-1 XXZ model. The effect of ground state, the free energy, the magnetic susceptibility, the specific heat and the Kondo temperature are given by using the thermodynamic Bethe ansatz equation.
In this paper, the Kondo magnetic effect is studied for the XXZ spin chain where the impurities are coupled to the edges of the system. The Hamiltonian of our model can be constructed from the transfer matrix. It is exactly solvable and the exchange constants between the bulk and the boundary impurities are arbitrary. The finite-size corrections to the ground-state energy are obtained for the magnetic impurities and the boundary condition. The specific heat and the susceptibility contributed by the impurities are derived and the Kondo temperature is given explicitly by the use of the Luttinger-Fermi liquid picture and the Bethe ansatz method.
The thermodynamics of finite open antiferromagnetic XXZ chains is studied using field theory, Bethe ansatz and quantum Monte Carlo methods. For the susceptibility a parameter-free result as a function of the number of sites L and temperature T beyond the scaling limit is derived. The limiting cases ( J being the exchange constant), where the boundary correction shows a logarithmically suppressed Curie behaviour, and , where a crossover to the ground state behaviour takes place, are discussed in detail. On the basis of this analysis we present a simple formula for the averaged susceptibility of a spin-1/2 chain doped with non-magnetic impurities. We show that the effective Curie constant has a highly non-trivial temperature dependence and shows scaling in the low temperature limit. Finally, corrections due to intrachain and interchain couplings and implications for experiments on Sr 2 Cu 1− x Pd x O 3+δ and related compounds are discussed.
We study exactly the effect of an impurity in the interacting quantum spin chain at low temperature by solving the integrable spin-1/2 XXZ periodic chain with an impurity through the algebraic and thermal Bethe ansatz methods. In particular, we investigate how the crossover temperature for the impurity specific heat depends on the impurity parameter, i.e. the coupling of the impurity to other spins, and show that it is consistent with the analytic expression that is obtained by setting the impurity susceptibility to be proportional to the inverse of the crossover temperature. In the model, two types of crossover behavior appear: one from the high-temperature regime to the low-temperature Kondo regime and another from the N -site homogeneous chain to the ( N − 1)-site chain with a decoupled free impurity spin, with respect to the temperature and the impurity parameter, respectively.
We consider the Heisenberg chain of spin 1/2 with a concentration x of impurity spins S. The thermodynamic Bethe ansatz equations are stated for this model. The ground-state equations are analyzed as a function of x and magnetic field. In zero field the ground state is a singlet for finite x, but non-Fermi-liquid-like for x\ensuremath{\rightarrow}0. Two energy bands play a role at T=0. The Van Hove singularities of the empty bands define two critical fields, Hc1(x) and Hc2(x), at which the susceptibility diverges. The non-Fermi-liquid behavior as x\ensuremath{\rightarrow}0 arises from nonanalyticities as Hc2 vanishes.
The numerical solution of the Bethe ansatz equations of an integrable SU(2)-invariant generalization of the spin-S antiferromagnetic Heisenberg chain (Takhtajian-Babujian model) with a spin-S' impurity in zero magnetic field is presented. The entropy, specific heat and susceptibility of an impurity of spin S' are obtained numerically as a function of the spin S of the chain. 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 (undercompensated) at T=0, leaving an effective spin of (S'-S); (iii) if S'