Sum rules for four-spinon dynamic structure factor in XXX model

Abstract

In the context of the antiferromagnetic spin 1/2 Heisenberg quantum spin chain (XXX model), we estimate the contribution of the exact four-spinon dynamic structure factor $S_4$ by calculating a number of sum rules the total dynamic structure factor $S$ is known to satisfy exactly. These sum rules are: the static susceptibility, the integrated intensity, the total integrated intensity, the first frequency moment and the nearest-neighbor correlation function. We find that the contribution of $S_4$ is between 1% and 2.5%, depending on the sum rule, whereas the contribution of the exact two-spinon dynamic structure factor $S_2$ is between 70% and 75%. This is consistent with the expected scattering weight of states from outside the spin-wave continuum. The calculations are numerical and Monte Carlo based. Good statistics are obtained.

arXiv comment21 pages, Revtex, 02 figures

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Cited by in corpus (2)

• The 4-spinon dynamical structure factor of the Heisenberg chain
• Spin-Dynamics of the antiferromagnetic S=1/2-Chain at finite magnetic Fields and intermediate Temperatures