Dimer and N\'eel order-parameter fluctuations in the spin-fluid phase of the s=1/2 spin chain with first and second neighbor couplings

TL;DR

This paper investigates the zero-temperature dynamical properties of a 1D s=1/2 spin chain with both nearest and next-nearest neighbor couplings, focusing on fluctuations of Neel and dimer order parameters using continued-fraction analysis.

Contribution

It provides a detailed analysis of the dynamic structure factors and excitation spectra in the spin-fluid phase of the model, revealing discrete excitation branches.

Findings

Identification of the dependence of spectral features on exchange constants.

Discovery of a discrete excitation branch above the spinon continuum.

Analysis of the spectral-weight distribution in key structure factors.

Abstract

The dynamical properties at T=0 of the one-dimensional (1D) s=1/2 nearest-neighbor (nn) XXZ model with an additional isotropic next-nearest-neighbor (nnn) coupling are investigated by means of the recursion method in combination with techniques of continued-fraction analysis. The focus is on the dynamic structure factors S_{zz}(q,\omega) and S_{DD}(q,\omega), which describe (for q=\pi) the fluctuations of the N\'eel and dimer order parameters, respectively. We calculate (via weak-coupling continued-fraction analysis) the dependence on the exchange constants of the infrared exponent, the renormalized bandwidth of spinon excitations, and the spectral-weight distribution in S_{zz}(\pi,\omega) and S_{DD}(\pi,\omega), all in the spin-fluid phase, which is realized for planar $nn$ anisotropy and sufficiently weak nnn coupling. For some parameter values we find a discrete branch of excitations above the spinon continuum. They contribute to S_{zz}(q,\omega) but not to S_{DD}(q,\omega).