Universal relation between the dispersion curve and the ground-state correlation length in one-dimensional antiferromagnetic quantum spin systems - art. no. 104432

We discuss a universal relation epsilon (i kappa) =0 with Re kappa= 1/xi in 1D quantum spin systems with an excitation gap, where epsilon (k) is the d ispersion curve of the low-energy excitation and xi is the correlation leng th of the ground state. We first discuss this relation for integrable model s such as the Ising model in a transverse filed and the XYZ model. We secon dly make a derivation of the relation for general cases, in connection with the equilibrium crystal shape in the corresponding 2D classical system. We finally verify the relation for the S=1 bilinear-biquadratic spin chain an d the S=1/2 zigzag spin ladder numerically.