Dynamics of the spin-half Heisenberg chain at intermediate temperatures

TL;DR

This paper investigates the spin-1/2 Heisenberg chain's dynamics across various temperatures using multiple computational methods, revealing temperature-dependent spectral features and confirming theoretical low-temperature scaling laws.

Contribution

It combines high-temperature expansions, recursion, and quantum Monte Carlo methods to analyze the dynamic structure factor and low-temperature scaling in the Heisenberg chain.

Findings

Low-temperature suppression of the low-frequency peak in the dynamic structure factor.

Development of two-spinon continuum features at low temperatures.

Confirmation of theoretical scaling laws for S(pi) and X(pi).

Abstract

Combining high-temperature expansions with the recursion method and quantum Monte Carlo simulations with the maximum entropy method, we study the dynamics of the spin-1/2 Heisenberg chain at temperatures above and below the coupling J. By comparing the two sets of calculations, their relative strengths are assessed. At high temperatures, we find that there is a low-frequency peak in the momentum integrated dynamic structure factor, due to diffusive long-wavelength modes. This peak is rapidly suppressed as the temperature is lowered below J. Calculation of the complete dynamic structure factor S(k,w) shows how the spectral features associated with the two-spinon continuum develop at low temperatures. We extract the nuclear spin-lattice relaxation rate 1/T1 from the w-->0 limit, and compare with recent experimental results for Sr2CuO3 and CuGeO3. We also discuss the scaling behavior of the dynamic susceptibility, and of the static structure factor S(k) and the static susceptibility X(k). We confirm the asymptotic low-temperature forms S(pi)~[ln(T)]^(3/2) and X(pi)~T^(-1)[ln(T)]^(1/2), expected from previous theoretical studies.