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Scientific article
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English

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

Published inSciPost physics, vol. 11, 055
Publication date2021-09-13
First online date2021-09-13
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.

Keywords
  • Field theory: conformal
  • Energy: low
  • Higher-order
  • Quenching
  • Liquid
  • Correlation function
  • Initial state
  • Factorization
  • Hubbard model
  • Rescaling
  • Scaling
  • Tube
  • Atom
  • Gas
NoteNew section with goal and main results included (1.1), further changes and explanations in sections 2 and 4
Research group
Funding
  • European Commission - New states of Entangled Matter Out of equilibrium [771536]
Citation (ISO format)
RUGGIERO, Paola et al. Quenches in initially coupled Tomonaga-Luttinger Liquids: a conformal field theory approach. In: SciPost physics, 2021, vol. 11, p. 055. doi: 10.21468/SciPostPhys.11.3.055
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Article (Published version)
accessLevelPublic
Identifiers
ISSN of the journal2542-4653
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