Quantum echo dynamics in the Sherrington-Kirkpatrick model
Abstract
Understanding the footprints of chaos in quantum-many-body systems has been under debate for a long time. In this work, we study the echo dynamics of the Sherrington-Kirkpatrick (SK) model with transverse field under effective time reversal. We investigate numerically its quantum and semiclassical dynamics. We explore how chaotic many-body quantum physics can lead to exponential divergence of the echo of observables and we show that it is a result of three requirements: i) the collective nature of the observable, ii) a properly chosen initial state and iii) the existence of a well-defined chaotic semi-classical (large-N) limit. Under these conditions, the echo grows exponentially up to the Ehrenfest time, which scales logarithmically with the number of spins N. In this regime, the echo is well described by the semiclassical (truncated Wigner) approximation. We also discuss a short-range version of the SK model, where the Ehrenfest time does not depend on N and the quantum echo shows only polynomial growth. Our findings provide new insights on scrambling and echo dynamics and how to observe it experimentally.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Aug 19, 2020
- Source ID
- 10.21468/scipostphys.9.2.021
Entities
People
- Alessandro Silva
- Anatoli Polkovnikov
- Silvia Pappalardi
Organizations
- Air Force Office of Scientific Research
- Boston University
- International Centre for Theoretical Physics
- International School for Advanced Studies
- National Science Foundation