We use a pseudofermion representation to investigate strong-field anomalies of the magnetic-field (h) dependence of the specific heat (c) of a spin-1/2 XY chain doped with magnetic impurities. If at certain magnetic field the impurity-induced split-off energy levels come sufficiently close to the chemical potential of pseudofermions (zero), then at low temperatures the specific heat of the chain is significantly altered by even a small number of impurities. The impurity-induced peaks of the c(h) dependence correspond to magnetic fields in a range where the specific heat of the ideal spin-1/2 XY chains is exponentially small. They have the same physical origin, but different structure, as compared to the high-field anomalies of longitudinal magnetic susceptibility investigated previously.
A Green's-function method is used to obtain the exact expression for the local susceptibility of the impure spin-1/2 XY chain at zero temperature. The presence of the impurity (or boundary) affects the singularity of the magnetic field dependence of the local susceptibility. The corresponding critical exponent changes from -1/2 to +1/2 at an arbitrary distance from the impurity site. In contrast with the transverse Ising model, the critical exponent is independent of the perturbation strength. This phenomenon is related to the spatial oscillations of the local density of states in the nonideal XY chain. It is also shown that experimental investigation of the field dependence of the finite-temperature macroscopic susceptibility of the one-dimensional XY-like system (such as
Cs2CoCl4) may reveal the formation of the localized states associated with impurities.
Using the bosonization technique, we have studied a spin-1/2 magnetic impurity in Heisenberg chain, and shown that the impurity specific heat and spin susceptibility have an anomalous temperature dependence. The temperature dependence of the impurity specific heat is ${C}_{\mathrm{im}}(T)\ensuremath{\sim}{T}^{\ensuremath{\mu}}$, $\ensuremath{\mu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4\ensuremath{-}\frac{1}{g}(1\ensuremath{-}g{)}^{2}$, for
gc<g<1. The impurity spin susceptibility has the following temperature dependence: ${\ensuremath{\chi}}_{\mathrm{im}}(T)\ensuremath{\sim}{T}^{\ensuremath{\nu}}$, $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3\ensuremath{-}\frac{1}{g}(1\ensuremath{-}g{)}^{2}$, for
gc<g<1, and $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}1$, for $g\ensuremath{\le}{g}_{c}$, where
gc satisfies ${4g}_{c}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}({1\ensuremath{-}g}_{c}{)}^{2}$, and
g is a dimensionless coupling strength parameter.
We study by Monte Carlo simulations a magnetic impurity coupled antiferromagnetically to a one-dimensional quantum spin model. The impurity susceptibility and the spin-correlation function are calculated. By defining and evaluating an energy scale from the inverse of the impurity susceptibility at zero temperature, we find a scaling relation for the impurity susceptibility in agreement with the prediction of the conformal field theory. We analyze the problem by mapping the spin model onto the resonant-level model, and interpret the energy scale as the resonant-level width. The spin-correlation function between the impurity spin and the spins in the chain is found to extend over long range at low temperatures. We show that the system can be considered as a model of an insulator with heavy-fermion behavior.
In the framework of the exactly solvable model, using nonperturbative methods, the temperature and magnetic field behavior of the NMR relaxation rate (and low-energy dynamical structure factor) for the antiferromagnetic Heisenberg spin-1/2 chain with magnetic impurities is calculated. For a single magnetic impurity, totally screened at low temperatures by spinons of the chain, the critical exponents, which determine the low-temperature and magnetic field behavior, get renormalized. For the finite concentration of impurities with the random distribution of the impurity-chain coupling the weak disorder in the distribution does not produce essential changes to the dynamical structure factor. Contrary, the strong disorder yields drastically different behavior of the low-energy dynamical characteristics, comparing to the homogeneous chain. Our results are generic, and they qualitatively agree in limiting cases with the results of perturbative calculations for disordered spin chains and with the data of experiments on quasi-one-dimensional spin compounds.
We study the effect of anisotropy of spin-
S impurities on an antiferromagnetic SU(2) Heisenberg chain. The magnetic impurities are assumed to have an XXZ-type anisotropic exchange with their neighboring sites. First, using density-matrix renormalization group technique, we examine spin-spin correlation function, instability of N\'eel order, and local spin susceptibility in the presence of a single spin-
S impurity. Based on the results, we find that the types of spin-
S impurities are classified into two groups: (i) nonmagnetic and
S=1 impurities enhance only short-range antiferromagnetic correlation and (ii)
S=21 and
S>1 impurities can, in contrast, stabilize a long-range N\'eel order in the disordered SU(2) Heisenberg chain. Then, we focus on the case of
S=21 impurity as a representative of (ii) and investigate the evolution of some experimentally observable quantities such as magnetization, specific heat, and magnetic susceptibility, as a function of concentration and XXZ anisotropy strength of the impurity. We confirm that the N\'eel order is induced in the bulk spin chain in the presence of finite amount of easy-axis XXZ
S=21 impurities. Furthermore, we recover some of the aforementioned features using cluster mean-field theory, which allows us to present results on experimentally accessible quantities at finite temperatures. Interestingly, in the presence of uniform magnetic field, the total magnetization exhibits a pseudogap behavior for low values of applied field. We also discuss the dependence of NMR spectrum on various XXZ impurities and identify that the spin state of Co impurity in
SrCu0.99Co0.01O2 is
S=23.