The characteristics of the nuclear magnetic resonance (NMR), the contributions to the spin-lattice relaxation rate, and Knight shift of the resonance position are calculated exactly for a model spin-
1/2 XY chain with the magnetic impurity. It is shown that the deviations of the impurity's coupling to the chain and the effective impurity's
g factor from the values in the host spin chain yield special features in the temperature and magnetic field behavior for these NMR characteristics. The role of impurity-induced local levels in the NMR low-energy spin dynamics of spin chains is determined.
In this work we consider several exactly solvable models of magnetic impurities in critical quantum antiferromagnetic spin chains and multichannel Kondo impurities. Their ground-state properties are studied, and the finite set of nonlinear integral equations which exactly describe the thermodynamics of the models is constructed. We obtain several analytical low-energy expressions for the temperature, magnetic field, and frequency dependences of important characteristics of exactly solvable disordered quantum spin models and disordered multichannel Kondo impurities with essential many-body interactions. We show that the only low-energy parameter that gets renormalized is the velocity of the low-lying excitations (or the effective crossover scale connected with each impurity); the others appear to be universal. In our study several kinds of strong disorder important for experiments were used. Some of them produce low divergences in certain characteristics of our strongly disordered critical systems (compared with finite values for the homogeneous case or a single impurity). For weak disorder, or for narrow distributions of the local Kondo temperatures, our exact results reveal the presence of Kondo screening of disordered ensembles of magnetic impurities by low-lying excitations of the host. We point out that our results qualitatively coincide with the data of experiments on real disordered quasi-one-dimensional antiferromagnetic systems and with the similar behavior of some heavy metallic alloys.
We calculate exactly the thermodynamics of ensembles of magnetic impurities with randomly distributed host-impurity couplings in the critical region of the uniaxial spin-1/2 quantum chain. We derive a finite set of integral equations describing the complete temperature and magnetic field dependence of the system. Exact numerical results for arbitrary values of temperature and external magnetic field are obtained. We show that for strong disorder the quenching of the impurity moments is absent. For weak disorder the screening persists, but with a critical non-Fermi-liquid behaviour of the magnetic susceptibility and specific heat. We point out that the `easy-plane' magnetic anisotropy does not qualitatively change the behaviour of the thermodynamic characteristics of the disordered impurities in the antiferromagnetic chain. On the other hand, anisotropy of ferromagnetic type can enhance the tendency to quenching of the impurities for strong disorder.
We present an exact theory that describes how magnetic impurities change the behavior of the thermal conductivity for the integrable Heisenberg antiferromagnetic quantum spin-1/2 chain. Single magnetic impurities and a large concentration of impurities with similar values of the couplings to the host chain (a weak disorder) do not change the linear-in-temperature low-T behavior of the thermal conductivity: Only the slope of that behavior becomes smaller, compared to the homogeneous case. The strong disorder in the distribution of the impurity-host couplings produces more rapid temperature growth of the thermal conductivity, compared to the linear-in-T dependence of the homogeneous chain and the chain with weak disorder. Recent experiments on the thermal conductivity in inhomogeneous quasi-one-dimensional quantum spin systems manifest qualitative agreement with our results.
We study dynamical properties at finite temperature
(T) of Heisenberg spin chains with random antiferromagnetic exchange couplings, which realize the random singlet phase in the low-energy limit, using three complementary numerical methods: exact diagonalization, matrix-product-state algorithms, and stochastic analytic continuation of quantum Monte Carlo results in imaginary time. Specifically, we investigate the dynamic spin structure factor $S(q,\ensuremath{\omega})$ and its $\ensuremath{\omega}\ensuremath{\rightarrow}0$ limit, which are closely related to inelastic neutron scattering and nuclear magnetic resonance (NMR) experiments (through the spin-lattice relaxation rate
1/T1). Our study reveals a continuous narrow band of low-energy excitations in $S(q,\ensuremath{\omega})$, extending throughout the
q space, instead of being restricted to $q\ensuremath{\approx}0$ and $q\ensuremath{\approx}\ensuremath{\pi}$ as found in the uniform system. Close to $q=\ensuremath{\pi}$, the scaling properties of these excitations are well captured by the random-singlet theory, but disagreements also exist with some aspects of the predicted
q dependence further away from $q=\ensuremath{\pi}$. Furthermore we also find spin diffusion effects close to
q=0 that are not contained within the random-singlet theory but give non-negligible contributions to the mean
1/T1. To compare with NMR experiments, we consider the distribution of the local relaxation rates
1/T1. We show that the local
1/T1 values are broadly distributed, approximately according to a stretched exponential. The mean
1/T1 first decreases with
T, but below a crossover temperature it starts to increase and likely diverges in the limit of a small nuclear resonance frequency ${\ensuremath{\omega}}_{0}$. Although a similar divergent behavior has been predicted and experimentally observed for the static uniform susceptibility, this divergent behavior of the mean
1/T1 has never been experimentally observed. Indeed, we show that the divergence of the mean
1/T1 is due to rare events in the disordered chains and is concealed in experiments, where the typical
1/T1 value is accessed.