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.

Quantum echo dynamics in the Sherrington-Kirkpatrick model / Pappalardi, Silvia; Polkovnikov, Anatoly; Silva, Alessandro. - In: SCIPOST PHYSICS. - ISSN 2542-4653. - 9:2(2020), pp. 1-31. [10.21468/SciPostPhys.9.2.021]

Quantum echo dynamics in the Sherrington-Kirkpatrick model

Silva, Alessandro
2020

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.
9
2
1
31
021
10.21468/SciPostPhys.9.2.021
https://www.scipost.org/SciPostPhys.9.2.021
https://arxiv.org/abs/1910.04769
Pappalardi, Silvia; Polkovnikov, Anatoly; Silva, Alessandro
File in questo prodotto:
File Dimensione Formato  
SciPostPhys_9_2_021.pdf

accesso aperto

Descrizione: pdf editoriale
Tipologia: Versione Editoriale (PDF)
Licenza: Creative commons
Dimensione 2.43 MB
Formato Adobe PDF
2.43 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/128618
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 8
  • ???jsp.display-item.citation.isi??? 8
social impact