Dimer and trimer fluctuations in thes=12transverseXXchain

Abstract

Exact results for the dynamic dimer and trimer structure factors of the one-dimensional $s=\frac{1}{2}\phantom{\rule{0.3em}{0ex}}XX$ model in a transverse magnetic field $(\ensuremath{\Vert}z)$ are presented and discussed in relation to known exact results for the dynamic spin structure factors. In the framework of the Jordan-Wigner representation, the accessible spectrum of the dimer fluctuation operator is limited to two-fermion excitations, whereas that of the trimer fluctuation operator involves two- and four-fermion excitations. The spectral boundaries, soft modes, and singularity structure of the four-fermion excitation continuum as probed by the dynamic trimer structure factor are examined and compared to corresponding properties of the two-fermion excitation continuum, as probed by the dynamic dimer and transverse spin structure factors.