Universal relation between the dispersion curve and the ground-state correlation length in one-dimensional antiferromagnetic quantum spin systems

摘要: We discuss a universal relation $\ensuremath{\varepsilon}(i\ensuremath{\kappa})=0$ with $\mathrm{Re}\ensuremath{\kappa}=1/\ensuremath{\xi}$ in 1D quantum spin systems an excitation gap, where $\ensuremath{\varepsilon}(k)$ is the dispersion curve of low-energy and $\ensuremath{\xi}$ correlation length ground state. first this for integrable models such as Ising model transverse filed $\mathrm{XYZ}$ model. secondly make derivation general cases, connection equilibrium crystal shape corresponding 2D classical system. finally verify $S=1$ bilinear-biquadratic chain $S=1/2$ zigzag ladder numerically.