A model of disordered spin-Peierls system is considered, where domain walls are randomly distributed as a telegraph noise. For this realization of the disorder in an XX spin chain, we calculate exactly the density of states as well as several thermodynamic quantities. The resulting physical behavior should be qualitatively unchanged even for an XXZ chain, up to the isotropic XXX point. For weak disorder, besides a high energy regime where the behavior of a pure spin-Peierls system is recovered, there is a crossover to a low energy regime with singular thermodynamic properties and enhanced antiferromagnetic fluctuations. These regimes are analyzed with the help of exact results, and the relevant energy scales determined. We discuss the possible relevance of such a disorder realization to the doped inorganic spin-Peierls compound ${\mathrm{CuGeO}}_{3}$.
A model of disordered spin-Peierls system is considered, where domain walls are randomly distributed as a telegraph noise. For this realization of the disorder in an XX spin chain, we calculate exactly the density of states as well as several thermodynamic quantities. The resulting physical behavior should be qualitatively unchanged even for an XXZ chain, up to the isotropic XXX point. For weak disorder, besides a high energy regime where the behavior of a pure spin-Peierls system is recovered, there is a crossover to a low energy regime with singular thermodynamic properties and enhanced antiferromagnetic fluctuations. These regimes are analyzed with the help of exact results, and the relevant energy scales determined. We discuss the possible relevance of such a disorder realization to the doped inorganic spin-Peierls compound CuGeO3.
We study a model of a spin-Peierls material consisting of a set of antiferromagnetic Heisenberg chains coupled with phonons and interacting among them via an interchain elastic coupling. The excitation spectrum is analyzed by bosonization techniques and the self-harmonic approximation. The elementary excitation is the creation of a localized domain structure where the dimerized order is the opposite to the one of the surroundings. It is a triplet excitation whose formation energy is smaller than the magnon gap. Magnetic internal excitations of the domain are possible and give the further excitations of the system. We discuss these results in the context of recent experimental measurements on the inorganic spin-Peierls compound CuGeO3.
The random antiferromagnetic spin-1∕2 XX and XXZ chain is studied numerically for varying strength of the disorder, using exact diagonalization and stochastic series expansion methods. The spin-spin correlation function as well as the stiffness display a clear crossover from the pure behavior (no disorder) to the infinite randomness fixed point or random singlet behavior predicted by the real space renormalization group. The crossover length scale is shown to diverge as $\ensuremath{\xi}\ensuremath{\sim}{\mathcal{D}}^{\ensuremath{-}\ensuremath{\gamma}}$, where D is the variance of the random bonds. Our estimates for the exponent $\ensuremath{\gamma}$ agrees well within the error bars with the one for the localization length exponent emerging within an analytical bosonization calculation. Exact diagonalization and stochastic series expansion results for the string correlation function are also presented.
The effect of dimerization on the random antiferomagnetic Heisenberg chain with spin 1/2 is studied by the density matrix renormalization group method. The ground state energy, the energy gap distribution and the string order parameter are calculated. Using the finite size scaling analysis, the dimerization dependence of the these quantities are obtained. The ground state energy gain due to dimerization behaves as u a with a > 2 where u denotes the degree of dimerization, suggesting the absence of spin-Peierls instability. It is explicitly shown that the string long range order survives even in the presence of randomness. The string order behaves as u 2β with β∼0.37 in agreement with the recent prediction of real space renormalization group theory (β=(3−5)/2≃0.382). The physical picture of this behavior in this model is also discussed.
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.
Concerning the question of the (spin-)Peierls mechanism in the presence of disorder we present a detailed analysis of the ground state phase diagram of the dimerized anisotropic Heisenberg-XXZ chain containing one impurity. It is obtained by studying the destruction of the quantum coherence by the perturbations. The stability of the Peierls phase, i. e. the occurence of a stable dimerization, is determined by the energy gain and gap due to the coupling to the static phonons. The extension of the paramagnetic phase, found already in the clean dimerized chain, grows by adding the impurity, because the distortions weaken each other. The Peierls phase is reduced for two reasons: First, the energy gain of the spin-system decreases, which leads to a smaller stable dimerization and second, the energy gap itself is reduced.
The spin-Peierls transition at TSP of spin-21 chains with isotropic exchange interactions has previously been modeled as correlated for T>TSP and mean field for T<TSP. We use correlated states throughout in the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model with antiferromagnetic exchange J1 and ${J}_{2}=\ensuremath{\alpha}{J}_{1}$ between first and second neighbors, respectively, and variable frustration $0\ensuremath{\le}\ensuremath{\alpha}\ensuremath{\le}0.50$. The thermodynamic limit is reached at high T by exact diagonalization of short chains and at low T by density matrix renormalization group calculations of progressively longer chains. In contrast to mean field results, correlated states of 1D models with linear spin-phonon coupling and a harmonic adiabatic lattice provide an internally consistent description in which the parameter TSP yields both the stiffness and the lattice dimerization $\ensuremath{\delta}(T)$. The relation between TSP and $\mathrm{\ensuremath{\Delta}}(\ensuremath{\delta},\ensuremath{\alpha})$, the T=0 gap induced by dimerization, depends strongly on $\ensuremath{\alpha}$ and deviates from the BCS gap relation that holds in uncorrelated spin chains. Correlated states account quantitatively for the magnetic susceptibility of TTF-CuS4C4(CF3)4 crystals (J1=79K, $\ensuremath{\alpha}=0$, TSP=12K) and CuGeO3 crystals (J1=160K, $\ensuremath{\alpha}=0.35$, TSP=14K). The same parameters describe the specific heat anomaly of CuGeO3 and inelastic neutron scattering. Modeling the spin-Peierls transition with correlated states exploits the fact that $\ensuremath{\delta}(0)$ limits the range of spin correlations at T=0 while T>0 limits the range at $\ensuremath{\delta}=0$.