We study quantum spin-1/2 Heisenberg ferromagnetic chains with dilute random antiferromagnetic impurity bonds with the modified spin-wave theory. By describing thermal excitations in the language of spin waves, we observe a low-temperature Curie susceptibility due to the formation of large spin clusters first predicted by the real-space renormalization-group approach, as well as a crossover to a pure ferromagnetic spin-chain behavior at intermediate and high temperatures. We compare our results of the modified spin-wave theory to quantum Monte Carlo simulations.
The low energy properties of the spin-1/2 random Heisenberg chain with ferromagnetic and antiferromagnetic interactions are studied by means of the density matrix renormalization group (DMRG) and real space renormalization group (RSRG) method for finite chains. The results of the two methods are consistent with each other. The deviation of the gap distribution from that of the random singlet phase and the formation of the large-spin state is observed even for relatively small systems. For a small fraction of the ferromagnetic bond, the effect of the crossover to the random singlet phase on the low temperature susceptibility and specific heat is discussed. The crossover concentration of the ferromagnetic bond is estimated from the numerical data.
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.
One-dimensional Heisenberg spin 1/2 chains with random ferro- and antiferromagnetic bonds are realized in systems such as
Sr3CuPt1−xIrxO6. We have investigated numerically the thermodynamic properties of a generic random bond model and of a realistic model of
Sr3CuPt1−xIrxO6 by the quantum Monte Carlo loop algorithm. For the first time we demonstrate the separation into three different temperature regimes for the original Hamiltonian based on an exact treatment, especially we show that the intermediate temperature regime is well-defined and observable in both the specific heat and the magnetic susceptibility. The crossover between the regimes is indicated by peaks in the specific heat. The uniform magnetic susceptibility shows Curie-like behavior in the high-, intermediate- and low-temperature regime, with different values of the Curie constant in each regime. We show that these regimes are overlapping in the realistic model and give numerical data for the analysis of experimental tests.
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 use linear spin wave theory and series expansion method to study the diluted quantum antiferromagnetic Heisenberg model at zero temperature near the p = 1 and p =
psbQ respectively, where p is the concentration of the spins or bonds, and
psbQ is the transition point from order to disorder of the quantum spin system. For the first case, our complete calculation to the first order in x
equiv 1
− p gives a dispersion relation for long-wavelength spin waves in the form
omega(vecq) =
c(x)q+igamma(x)qsptau. Our results for
c(x) agrees with previous work, where
c(x) =
c(0)lbrack1−alphax+O(xsp2)rbrack. In particular the coefficient
alpha, which can be related to the helicity modulus and the uniform perpendicular susceptibility, diverges in the limit
dto2. One major new results is that
tau =
d−1, which means that d = 2 is the lower critical dimension at which infrared divergences affect the dynamical response due to vacancies. For the second case, the critical behavior of the quantum system near
psbQ is found to be different from that of the percolation and pure systems. Thus there exists a new fixed point in the phase diagram, which specifies a new universality class. The correlation length exponents
nu (which comes from the relation
xisim(psbQ−p)spnu, where
xi is the correlation length) are estimated, which are 0.65
pm 0.2 and 0.55
pm 0.2 in 2 and 3 dimensions respectively. The exponents of crossover with temperature and time are determined. We also find evidence that
psbQ>psbc.