Edge singularities in high-energy spectra of gapped one-dimensional magnets in strong magnetic fields

TL;DR

This study reveals high-energy edge singularities in the spectra of gapped 1D magnets under strong magnetic fields, showing their relation to Tomonaga-Luttinger liquid behavior and extending understanding of spectral responses.

Contribution

It demonstrates the existence of high-energy edge singularities in the dynamical structure factor of gapped 1D spin systems in strong magnetic fields, linking them to Tomonaga-Luttinger liquid properties.

Findings

High-energy edge singularities are present in the spectrum.

The edge singularities follow a power-law behavior.

The edge features depend on the magnetic field strength.

Abstract

We use the dynamical density matrix renormalization group technique to show that the high-energy part of the spectrum of a S=1 Haldane chain, placed in a strong external magnetic field $H$ exceeding the Haldane gap $\Delta$, contains edge singularities, similar to those known to exist in the low-energy spectral response. It is demonstrated that in the frequency range $\omega\gtrsim \Delta$ the longitudinal (with respect to the applied field) dynamical structure factor is dominated by the power-law singularity $S^{\parallel}(q=\pi,\omega)\propto(\omega-\omega_{0})^{-\alpha'}$. We study the behavior of the high-energy edge exponent $\alpha'$ and the edge $\omega_{0}$ as functions of the magnetic field. The existence of edge singularities at high energies is directly related to the Tomonaga-Luttinger liquid character of the ground state at $H>\Delta$ and is expected to be a general feature of one-dimensional gapped spin systems in high magnetic fields.