The ground state for S 0 =1 and the low-lying excited states including localized states for S 0 =1/2 of a linear Heisenberg ferromagnet of spin 1/2 containing an antiferromagnetic impurity spin are calculated, where S 0 is a magnitude of the impurity spin. In these cases they belong to the subspace spanned by the two spin deviation kets. The two magnon states are solved. The method is based on the excitation from the rigorous one magnon localized state. The wave functions and the averages of the Z component of each spin are calculated. Numerical calculations for a ring consisting of twelve spins are performed. The results are in good agreement with analytical results for the ground state energy and localized levels.
Magnetic impurities coupled antiferromagnetically to a one-dimensional Heisenberg model are studied by numerical diagonalization of chains of finite clusters. By calculating the binding energy and the correlation function, it is shown that a local singlet develops around each impurity. This holds true for systems with a single impurity, with two impurities, and for impurities forming a lattice. The local character of the singlet is found to be little affected by the presence of other impurity spins. A small effective interaction is found between a pair of impurity spins, which oscillates depending on impurity distances. For impurity lattices, the energy spectrum shows a gap which is found to be much smaller than the binding energy per impurity if the coupling constants are small. For larger coupling constants, it increases to the same order of magnitude as the binding energy, indicating that a local singlet is broken to create excited states. Impurity lattices with ferromagnetic couplings are also studied and their connection to the Haldane problem is discussed.
The effect of impurities on the spectrum of one-magnon excitations of two quasi-one-dimensional spin systems—a double XY chain with an impurity atom and an analogous chain with an impurity link, in which two identical impurity atoms occupy neighboring nodes on different XY chains—is studied. The conditions for the existence of impurity levels and their number are determined for the system with one impurity, and for the system with an impurity link the explicit expressions for the energy and wave functions of localized states are also determined.
We investigate the effect of a magnetic field supported at a single lattice site on the low-energy spectrum of the ferromagnetic Heisenberg XXZ chain. Such fields, caused by impurities, can modify the low-energy spectrum significantly by pinning certain excitations, such as kink and droplet states. We distinguish between different boundary conditions (or sectors), the direction and also the strength of the magnetic field. E.g., with a magnetic field in the z direction applied at the origin and ++ boundary conditions, there is a critical field strength
Bc (which depends on the anisotropy of the Hamiltonian and the spin value) with the following properties: for
B<Bc there is a unique ground state with a gap, at the critical value
Bc there are infinitely many (droplet) ground states with gapless excitations, and for
B>Bc there is again a unique ground state but now belonging to the continuous spectrum. In contrast, any magnetic field with a nonvanishing component in the
xy plane yields a unique ground state, which, depending on the boundary conditions, is either an (anti)kink, or an (anti)droplet state. For such fields, i.e., not aligned with the z axis, excitations always have a gap and we obtain a rigorous lower bound for that gap.
The effect of a magnetic (S=1/2) impurity coupled to a two-dimensional system of correlated electrons (described by the t-J model) is studied by exact diagonalizations. It is found that, if the exchange coupling of the impurity with the neighboring spins is ferromagnetic or weakly antiferromagnetic, an extra hole can form bound states of different spatial symmetries with the impurity extending to a few lattice spacings. The binding energy is maximum when the impurity is completely decoupled (vacancy) and vanishes for an antiferromagnetic coupling exceeding \ensuremath{\sim}0.3J. Several peaks appear in the single-hole spectral function below the lower edge of the quasiparticle band as signatures of the d-, s-, and p-wave bound states.
We investigate the boundary effects that arise when spin-
21 impurities interact with the edges of the antiferromagnetic spin-
21 Heisenberg chain through spin exchange interactions. We consider both cases when the couplings are ferromagnetic or anti-ferromagnetic. We find that in the case of antiferromagnetic interaction, when the impurity coupling strength is much weaker than that in the bulk, the impurity is screened in the ground state via the Kondo effect. The Kondo phase is characterized by the Lorentzian density of states and dynamically generated Kondo temperature
TK. As the impurity coupling strength increases,
TK increases until it reaches its maximum value
T0=2πJ which is the maximum energy carried by a single spinon. When the impurity coupling strength is increased further, we enter another phase, the bound mode phase, where the impurity is screened in the ground state by a single particle bound mode exponentially localized at the edge to which the impurity is coupled. We find that the impurity can be unscreened by removing the bound mode. There exists a boundary eigenstate phase transition between the Kondo and the bound-mode phases, a transition which is characterized by the change in the number of towers of the Hilbert space. The transition also manifests itself in ground state quantities like local impurity density of states and the local impurity magnetization. When the impurity coupling is ferromagnetic, the impurity is unscreened in the ground state; however, when the absolute value of the ratio of the impurity and bulk coupling strengths is greater than
54, the impurity can be screened by adding a bound mode that costs energy greater than
T0. When two impurities are considered, the phases exhibited by each impurity remain unchanged in the thermodynamic limit, but nevertheless the system exhibits a rich phase diagram.