Quantum-critical scaling and temperature-dependent logarithmic corrections in the spin-half Heisenberg chain

TL;DR

This paper develops a new analytical approach to study the low-temperature dynamics of the spin-half Heisenberg chain, incorporating logarithmic corrections, and provides formulas that align well with experimental data.

Contribution

It introduces a generalized conformal mapping method to include logarithmic factors in correlation functions, improving theoretical predictions for the Heisenberg chain's dynamics.

Findings

Derived closed-form expressions for susceptibility and NMR rates.

Logarithmic corrections significantly affect scaling behavior.

Numerical results confirm the robustness of these corrections.

Abstract

Low temperature dynamics of the S=1/2 Heisenberg chain is studied via a simple ansatz generalizing the conformal mapping and analytic continuation procedures to correlation functions with multiplicative logarithmic factors. Closed form expressions for the dynamic susceptibility and the NMR relaxation rates 1/T_1 and 1/T_{2G} are obtained, and are argued to improve the agreement with recent experiments. Scaling in q/T and \omega/T are violated due to these logarithmic terms. Numerical results show that the logarithmic corrections are very robust. While not yet in the asymptotic low temperature regime, they provide striking qualitative confirmation of the theoretical results.