We study the quantum quench in two coupled Tomonaga-Luttinger Liquids (TLLs), from the off-critical to the critical regime, relying on the conformal field theory approach and the known solutions for single TLLs. We consider a squeezed form of the initial state, whose low energy limit is fixed in a way to describe a massive and a massless mode, and we encode the non-equilibrium dynamics in a proper rescaling of the time. In this way, we compute several correlation functions, which at leading order factorize into multipoint functions evaluated at different times for the two modes. Depending on the observable, the contribution from the massive or from the massless mode can be the dominant one, giving rise to exponential or power-law decay in time, respectively. Our results find a direct application in all the quench problems where, in the scaling limit, there are two independent massless fields: these include the Hubbard model, the Gaudin-Yang gas, and tunnel-coupled tubes in cold atoms experiments.

Quenches in initially coupled Tomonaga-Luttinger Liquids: a conformal field theory approach / Ruggiero, Paola; Calabrese, Pasquale; Foini, Laura; Giamarchi, Thierry Ange Jean-Marie. - In: SCIPOST PHYSICS. - ISSN 2542-4653. - 11:3(2021), pp. 1-37. [10.21468/SciPostPhys.11.3.055]

Quenches in initially coupled Tomonaga-Luttinger Liquids: a conformal field theory approach

Paola Ruggiero;Pasquale Calabrese;Laura Foini;Thierry Giamarchi
2021

Abstract

We study the quantum quench in two coupled Tomonaga-Luttinger Liquids (TLLs), from the off-critical to the critical regime, relying on the conformal field theory approach and the known solutions for single TLLs. We consider a squeezed form of the initial state, whose low energy limit is fixed in a way to describe a massive and a massless mode, and we encode the non-equilibrium dynamics in a proper rescaling of the time. In this way, we compute several correlation functions, which at leading order factorize into multipoint functions evaluated at different times for the two modes. Depending on the observable, the contribution from the massive or from the massless mode can be the dominant one, giving rise to exponential or power-law decay in time, respectively. Our results find a direct application in all the quench problems where, in the scaling limit, there are two independent massless fields: these include the Hubbard model, the Gaudin-Yang gas, and tunnel-coupled tubes in cold atoms experiments.
11
3
1
37
055
10.21468/SciPostPhys.11.3.055
http://arxiv.org/abs/2103.08927v3
Ruggiero, Paola; Calabrese, Pasquale; Foini, Laura; Giamarchi, Thierry Ange Jean-Marie
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/20.500.11767/128400
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 6
  • ???jsp.display-item.citation.isi??? 5
social impact