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

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

2005-05-24

arxiv.org/abs/cond-mat/0505594v1

Physics

Condensed Matter

Strongly Correlated Electrons

21 pages, Revtex, 02 figures

Scientific paper

10.1016/j.physb.2005.08.015

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.

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