Quantum nonintegrability in finite systems

Stefan Weigert

Gerhard H. Muller, J. C. Bonner, John B. Parkinson

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.

Emil A. Yuzbashyan, B. Sriram Shastry

HyungWon Kim, David A. Huse

We study the time evolution of the entanglement entropy of a one-dimensional nonintegrable spin chain, starting from random nonentangled initial pure states. We use exact diagonalization of a nonintegrable quantum Ising chain with transverse and longitudinal fields to obtain the exact quantum dynamics. We show that the entanglement entropy increases linearly with time before finite-size saturation begins, demonstrating a ballistic spreading of the entanglement, while the energy transport in the same system is diffusive. Thus, we explicitly demonstrate that the spreading of entanglement is much faster than the energy diffusion in this nonintegrable system.

Keiji Saito, Shinji Takesue, Seiji Miyashita

We numerically investigate thermal conduction in quantum dynamics. A one-dimensional quantum spin system is used as a model, which we can make integrable or nonintegrable by controlling parameter values. A different method to simulate heat reservoirs is introduced. Using this method, we perform numerical simulations of the spin chain in contact with two heat reservoirs at different temperatures. As a consequence, a flat temperature profile is observed in the integrable case, while a finite temperature gradient is found in a nonintegrable system. This result suggests that the Fourier heat law may be realized in nonintegrable systems and is consistent with the classical case reported in the literature. \textcopyright{} 1996 The American Physical Society.

L. E. Reichl