Edge Logarithmic Corrections probed by Impurity NMR

Semi-infinite quantum spin chains display spin autocorrelations near the boundary with power-law exponents that are given by boundary conformal field theories. We show that NMR measurements on spinless impurities that break a quantum spin chain lead to a spin-lattice relaxation rate 1/T_1^edge that has a temperature dependence which is a direct probe of the anomalous boundary exponents. For the antiferromagnetic S=1/2 spin chain, we show that 1/T_1^edge behaves as T (log T)^2 instead of (log T)^1/2 for a bulk measurement. We show that, in the case of a one-dimensional conductor described by a Luttinger liquid, a similar measurement leads to a relaxation rate 1/T_1^{edge} behaving as T, independent of the anomalous exponent K_rho.