Magnons in a one-dimensional spin glass: The high-field and zero-field limits

The high-field and zero-field behavior of the linearized magnetic excitations (harmonic magons) in a one-dimensional ±{}J Heisenberg spin glass are studied. In the high-field limit---a field strong enough to ensure complete alignment of the ground state---the density of states (DOS), the inverse localization length (ILL), and the dynamic structure factor are calculated over the interval -4JE-H4J (H is applied field) by employing the coherent-exchange approximation (CEA), negative-eigenvalue counting, and matrix diagonalization. In the low-energy regime (0.001E-H0.1J), the CEA closely approximates the exact results reproducing, in particular, the anomalous power-law behavior of the DOS {ρ}(E){~}(E-H)1/3 and the ILL 1/L(E){~}(E-H)2/3 for the symmetric distribution of the exchange interactions (concentration c=0.5). In zero field, the DOS and the ILL are calculated using negative-eigenvalue counting for 0E4J and 0.0001E0.01J. For c=0.5, a connection is established between the zero-field and the high-field limits, and for other concentrations, a phenomenological approach is developed in the low-energy regime where it is found that {ρ}(E)=f(c)E^-1/3 and 1/L(E)=g(c)E2/3.