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

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 $Δ$, contains edge singularities, similar to those known to exist in the low-energy spectral response. It is demonstrated that in the frequency range $ω\gtrsim Δ$ the longitudinal (with respect to the applied field) dynamical structure factor is dominated by the power-law singularity $S^{\parallel}(q=π,ω)\propto(ω-ω_{0})^{-α'}$. We study the behavior of the high-energy edge exponent $α'$ and the edge $ω_{0}$ 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 $H>Δ$ and is expected to be a general feature of one-dimensional gapped spin systems in high magnetic fields.