Edge Logarithmic Corrections Probed by Impurity NMR

Abstract

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 $1/{T}_{1}^{\mathrm{edge}}$ that has a temperature dependence which is a direct probe of the anomalous boundary exponents. For the antiferromagnetic $S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2$ spin chain, we show that $1/{T}_{1}^{\mathrm{edge}}\ensuremath{\propto}T{log}^{2}T$ 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 $1/{T}_{1}^{\mathrm{edge}}\ensuremath{\propto}T$, independent of the exponent ${K}_{\ensuremath{\rho}}$.