Nature of Quantum Chaos in Spin Systems

A novel concept for quantum chaos in spin systems is proposed which differs distinctively from concepts currently in use. It is argued (a) that the definition of quantum chaos cannot be based on the correspondence principle and (b) that quantum chaos is not equivalent to statistical behavior. Quantum chaos in spin systems implies the existence of a new type of spectrum consisting of excitations which do not form regular patterns with a multiparameter continuum structure in the thermodynamic limit, thus removing the constraint imposed by van Hove singularities that time-dependent correlation functions for pure quantum states cannot decay more rapidly than as powers of t. The irregular spectrum is caused by strong level repulsion resulting from the lack of a sufficient number of conservation laws in nonintegrable quantum many-body systems. The similarities and differences between quantum and classical chaos and, more generally, between quantum (non)integrability and classical (non)integrability are discussed in detail