QUANTUM CHAOS IN SPIN-FERMION MODELS

The full spectrum of a single hole in a quantum antiferromagnetic background (t-J(z)-J(perpendicular-to) model) is obtained by complete exact diagonalization of small two-dimensional clusters. Various statistical properties of the spectrum are investigated. On a very wide range of the parameters the level-spacing distribution follows a Gaussian-orthogonal-ensemble Wigner law characteristic of chaotic spectra. At small separation, the spectral rigidity follows the universal behavior described by random-matrix theory and presents deviations at higher energies. We argue that quantum chaos is a generic feature of complex (i.e., nonintegrable) strongly correlated fermion systems.