Dynamic probes of quantum spin chains with the Dzyaloshinskii-Moriya interaction

Abstract

We consider the spin-$\frac{1}{2}$ anisotropic $XY$ chain in a transverse $(z)$ field with the Dzyaloshinskii-Moriya interaction directed along the $z$ axis in spin space to examine the effect of the Dzyaloshinskii-Moriya interaction on the $zz$, $xx$, and $yy$ dynamic structure factors. Using the Jordan-Wigner fermionization approach we analytically calculate the dynamic transverse spin structure factor. It is governed by a two-fermion excitation continuum. We analyze the effect of the Dzyaloshinskii-Moriya interaction on the two-fermion excitation continuum. Other dynamic structure factors which are governed by many-fermion excitations are calculated numerically. We discuss how the Dzyaloshinskii-Moriya interaction manifests itself in the dynamic properties of the quantum spin chain at various fields and temperatures.