Quantum irregular spectrum in a corresponding classically chaotic lattice spin system

Abstract

The quantum spectrum is studied in a corresponding classically nonintegrable triangular three-spin system with antiferromagnetic exchange coupling. A critical energy ${\mathrm{E}}_{\mathrm{c}}$ is identified numerically. Irregularly distributed (bandlike) levels and well-separated clusters of (localized) levels appear below and above ${\mathrm{E}}_{\mathrm{c}}$, respectively. The statistical average of second-order differences of eigenvalues shows a scaling behavior when the spin magnitude is increased towards +\ensuremath{\infty}.