Dimer and trimer fluctuations in the s=1/2 transverse XX chain

TL;DR

This paper provides exact analytical results for the dynamic dimer and trimer structure factors in the one-dimensional s=1/2 XX model under a transverse magnetic field, highlighting differences in excitation spectra.

Contribution

It presents the first exact calculations of the dynamic dimer and trimer structure factors, analyzing their spectral boundaries and singularities within the Jordan-Wigner framework.

Findings

Dimer fluctuations involve only two-fermion excitations.

Trimer fluctuations include both two- and four-fermion excitations.

Spectral boundaries and singularities differ between dimer and trimer excitations.

Abstract

Exact results for the dynamic dimer and trimer structure factors of the one-dimensional s=1/2 XX model in a transverse magnetic field ($\parallel z$) 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-fermion 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 with corresponding properties of the two-fermion excitation continuum, as probed by the dynamic dimer and transverse spin structure factors.