Nonintegrability and quantum spin chains

Abstract

This study concerns the concept of nonintegrability in quantum many-body systems, which is related to the important and unresolved problem of quantum chaos. Our findings strongly indicate that nonintegrability affects the reliability of many approximation techniques which have proved to be successful in the study of integrable models. This report is based on finite-size studies of the low-lying spectral excitations of both integrable and nonintegrable 1D quantum spin models. In integrable cases, the characteristic excitation pattern of the infinite system is apparent even in relatively short chains. This is generally not the case in nonintegrable systems where we observe several classes of excitations with qualitatively different character. In some situations, the nature of the lowest-lying excitations actually changes with increasing system size, which makes finite-size studies very vulnerable to misleading conclusions if care is not taken.