Boundary logarithmic corrections to the dynamical correlation functions of one-dimensional spin-1/2 chains

TL;DR

This paper investigates the boundary dynamical correlations in one-dimensional spin-1/2 chains, revealing a logarithmic correction with an exponent of 1, derived analytically and confirmed numerically, enhancing understanding of boundary critical behavior.

Contribution

The paper provides the first analytical derivation of the logarithmic correction exponent for boundary correlations in the Heisenberg chain, confirmed by numerical data.

Findings

Logarithmic correction exponent λ=1 for boundary correlations.

Analytical derivation using renormalization group techniques.

Numerical confirmation via quantum Monte Carlo simulations.

Abstract

The asymptotic dynamical correlation functions in one-dimensional spin chains are described by power-laws. The corresponding exponents characterize different bulk and boundary critical behavior. We present novel results for the logarithmic contribution to the boundary correlations of an isotropic Heisenberg chain. The exponent of the logarithm, $\lambda=1$, is derived using a renormalization group technique. We confirm our analytical results by comparing with numerical quantum Monte Carlo data.