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 an S=1 Heisenberg 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 greater than or similar to Delta the longitudinal (with respect to the applied field) dynamical structure factor is dominated by the power-law singularity S-parallel to(q=pi,omega)proportional to(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.