Correlation amplitude for S=1/2 XXZ spin chain in the critical region

TL;DR

This paper uses numerical techniques to accurately determine correlation amplitudes in the critical S=1/2 XXZ spin chain, confirming recent theoretical conjectures and analyzing finite-size effects.

Contribution

It provides precise numerical estimates of correlation amplitudes in the gapless regime, validating recent theoretical predictions and analyzing logarithmic corrections.

Findings

Confirmed the exact amplitude conjectured by Lukyanov and Zamolodchikov.

Provided numerical estimates of correlation functions in the thermodynamic limit.

Analyzed logarithmic corrections in the Heisenberg model.

Abstract

The density-matrix renormalization-group technique is used to calculate the spin correlation functions <S^x_jS^x_k> and <S^z_jS^z_k> of the one-dimensional S=1/2 XXZ model in the gapless regime. The numerical results for open chains of 200 spins are analyzed by comparing them with correlation functions calculated from a low-energy field theory. This gives precise estimates of the amplitudes of the correlation functions in the thermodynamic limit. The exact amplitude recently conjectured by Lukyanov and Zamolodchikov and the logarithmic correction in the Heisenberg model are confirmed numerically.