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/T₁^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/T₁^edge ∝ T log² T instead of log^1/2 T for a bulk measurement. We show that, for a one-dimensional conductor described by a Luttinger liquid, a similar measurement leads to a rate 1/T₁^edge ∝ T, independent of the exponent K_ఱ.