Edge Logarithmic Corrections probed by Impurity NMR

TL;DR

This paper demonstrates how impurity NMR can directly probe boundary conformal field theory exponents in quantum spin chains and Luttinger liquids through distinctive temperature dependencies of the relaxation rate.

Contribution

It introduces a novel NMR measurement technique on impurities to directly access boundary exponents in quantum spin chains and Luttinger liquids.

Findings

For antiferromagnetic S=1/2 chains, 1/T_1^edge ~ T(log T)^2.

In Luttinger liquids, 1/T_1^edge ~ T, independent of the Luttinger parameter.

Boundary impurity NMR reveals boundary conformal field theory effects.

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^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.