Quantum chaos in spin-fermion models

The full spectrum of a single hole in a quantum antiferromagnetic background (t-Jₙ-J_ 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 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. Our results suggest that random-matrix theory might be useful to investigate the incoherent part of dynamical correlation functions (such as the hole spectral density or the spin structure factor).