Re acute accent nyi entropies are conceptually valuable and experimentally relevant generalizations of the celebrated von Neumann entanglement entropy. After a quantum quench in a clean quantum many-body system they generically display a universal linear growth in time followed by saturation. While a finite subsystem is essentially at local equilibrium when the entanglement saturates, it is genuinely out of equilibrium in the growth phase. In particular, the slope of the growth carries vital information on the nature of the system's dynamics, and its characterization is a key objective of current research. Here we show that the slope of Re acute accent nyi entropies can be determined by means of a spacetime duality transformation. In essence, we argue that the slope coincides with the stationary density of entropy of the model obtained by exchanging the roles of space and time. Therefore, very surprisingly, the slope of the entanglement is expressed as an equilibrium quantity. We use this observation to find an explicit exact formula for the slope of Re acute accent nyi entropies in all integrable models treatable by thermodynamic Bethe ansatz and evolving from integrable initial states. Interestingly, this formula can be understood in terms of a quasiparticle picture only in the von Neumann limit.

Growth of R??nyi Entropies in Interacting Integrable Models and the Breakdown of the Quasiparticle Picture / Bertini, B.; Klobas, K.; Alba, V.; Lagnese, G.; Calabrese, P.. - In: PHYSICAL REVIEW. X. - ISSN 2160-3308. - 12:3(2022). [10.1103/physrevx.12.031016]

Growth of R??nyi Entropies in Interacting Integrable Models and the Breakdown of the Quasiparticle Picture

Bertini, B.
;
Klobas, K.;Alba, V.;Lagnese, G.;Calabrese, P.
2022-01-01

Abstract

Re acute accent nyi entropies are conceptually valuable and experimentally relevant generalizations of the celebrated von Neumann entanglement entropy. After a quantum quench in a clean quantum many-body system they generically display a universal linear growth in time followed by saturation. While a finite subsystem is essentially at local equilibrium when the entanglement saturates, it is genuinely out of equilibrium in the growth phase. In particular, the slope of the growth carries vital information on the nature of the system's dynamics, and its characterization is a key objective of current research. Here we show that the slope of Re acute accent nyi entropies can be determined by means of a spacetime duality transformation. In essence, we argue that the slope coincides with the stationary density of entropy of the model obtained by exchanging the roles of space and time. Therefore, very surprisingly, the slope of the entanglement is expressed as an equilibrium quantity. We use this observation to find an explicit exact formula for the slope of Re acute accent nyi entropies in all integrable models treatable by thermodynamic Bethe ansatz and evolving from integrable initial states. Interestingly, this formula can be understood in terms of a quasiparticle picture only in the von Neumann limit.
2022
12
3
031016
10.1103/physrevx.12.031016
https://arxiv.org/abs/2203.17264
Bertini, B.; Klobas, K.; Alba, V.; Lagnese, G.; Calabrese, P.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

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/20.500.11767/131443
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 27
  • ???jsp.display-item.citation.isi??? 18
social impact