Non-magnetic impurities break a quantum spin chain into finite segments and induce Friedel-like oscillations in the local susceptibility near the edges. The signature of these oscillations has been observed in Knight shift experiments on the high-temperature superconductor YBa 2 Cu 3 O 6.5 and on the spin chain compound Sr 2 CuO 3 . Here we analytically calculate NMR spectra, compare with the available experimental data for Sr 2 CuO 3 , and show that the interchain coupling is responsible for the complicated and so far unexplained lineshape. Our results are based on a parameter-free formula for the local susceptibility of a finite spin chain obtained by bosonization which is checked by comparing with quantum Monte Carlo and density matrix renormalization group calculations.
The superfluid density of overdoped La
2−xSr
xCuO
4 thin films of high quality have been measured with Tc (defined by the onset of the Meissner effect) from 5.1 to 41.6 K by Bosovic et al. Given this Tc the superfluid density shows no clear evidence of critical fluctuations and no indication of vortex unbinding as T->Tc. Nevertheless, the superfluid density displays the expected behavior for for a quantum phase transition (QPT) in the (3+1)D-xy universality class, rho(T=0)~Tc^2. However, this relation is also a hallmark of dirty superconductors, treated in the mean-field approximation. Here we attempt to clear out the nature of the suppression of ro(T) as Tc->0. Noting that for any finite system the continuous transition will be rounded we perform a finite size scaling analysis. It uncovers that the ro(T) data data are consistent with a finite length limited 3D-xy transition. In some films it is their thickness and in others their inhomogeneity that determines the limiting length. Having established the precondition for the occurrence of a QPT mapping on the (3+1) D-xy model, we explore the consistency with the hallmarks of this transition. In particular with the relations rho(T)/rho(0)=1-ycT/Tc, rho((0)^Tc^2, yc=alpha*Tc/ro(0), where alpha is the coefficient in rho(T)=rho(0)-alphaT as T->0. The emerging agreement with these characteristics points clearly to a quantum fluctuations induced suppression, revealing the crossover from the thermal to the quantum critical regime as Tc ->0. In the classical-quantum mapping it corresponds to a 3D to (3 + 1)D crossover.