Scrambling and operator entanglement in local non-Hermitian quantum systems

Journal Article · Sun Oct 01 00:00:00 EDT 2023 · Phys.Rev.B

DOI:https://doi.org/10.1103/PhysRevB.108.134305· OSTI ID:1988474

Barch, Brian ^[1]; Anand, Namit ^[2]; Marshall, Jeffrey ^[3]; Rieffel, Eleanor ^[4]; Zanardi, Paolo ^[1]

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1. Southern California U.
2. NASA, Ames; Unlisted, US, TX
3. NASA, Ames; RIACS, Mtn. View
4. NASA, Ames

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.

• Research Organization: NASA, Ames; RIACS, Mtn. View; Southern California U.; Unlisted, US, TX
• Sponsoring Organization: US Department of Energy
• Grant/Contract Number: 89243024CSC000002; AC02-07CH11359
• OSTI ID: 1988474
• Report Number(s): FERMILAB-PUB-23-270-SQMS-V; oai:inspirehep.net:2661613; arXiv:2305.12054
• Journal Information: Phys.Rev.B, Journal Name: Phys.Rev.B Journal Issue: 13 Vol. 108
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
dynamical phase transitions
non-Hermitian systems
nonequilibrium systems
open quantum systems
quantum chaos
quantum entanglement