Scrambling and operator entanglement in local non-Hermitian quantum systems
ORAL
Abstract
The breakdown of Lieb-Robinson bounds in local, non-Hermitian quantum systems opens up the possibility for a rich landscape of quantum many-body phenomenology. We elucidate this by studying information scrambling and quantum chaos in non-Hermitian variants of paradigmatic local quantum spin-chain models. We utilize a mixture of exact diagonalization and tensor network techniques for our numerical results and focus on three dynamical quantities: (i) out-of-time-ordered correlators (OTOCs), (ii) operator entanglement of the dynamics, and (iii) entanglement growth following a quench from product initial states. We show that while OTOCs fail to capture information scrambling in a simple, local, non-Hermitian transverse-field Ising model, the closely related operator entanglement is a robust measure of dynamical properties of interest. Moreover, we show that the short-time growth of operator entanglement can generically detect entanglement phase transitions in these systems while its long-time average is shown to be a reliable indicator of quantum chaos and entanglement phases. This allows us to extend operator entanglement-based diagnostics from previous works on closed and open quantum systems, to the new arena of monitored quantum dynamics. Finally, we remark on the efficacy of these dynamical quantities in detecting integrability/chaos in the presence of continuous monitoring.
*N.A. is a KBR employee under the Prime Contract No. 80ARC020D0010 with NASA Ames Research Center. The authors acknowledge the USC CARC for providing computing resources. The authors acknowledge partial support from NSF Award No. PHY-1819189. This research was partially sponsored by the Army Research Office and Grant No. W911NF-20-1-0075. J.M. is thankful for support from NASA Academic Mission Services, Contract No. NNA16BD14C. The NASA team's work (N.A., J.M., E.R.) was primarily funded by DARPA under IAA 8839 Annex 129, while the material on applications to simulation is based upon work supported by the U.S. DOE, Office of Science, National Quantum Information Science Research Centers, SQMS under Contract No. DE-AC02-07CH11359 through NASA-DOE interagency agreement SAA2-403602.
