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

by Paola Ruggiero, Pasquale Calabrese, Laura Foini, Thierry Giamarchi

Submission summary

As Contributors: Paola Ruggiero
Preprint link: scipost_202103_00028v1
Date submitted: 2021-03-28 12:36
Submitted by: Ruggiero, Paola
Submitted to: SciPost Physics
Academic field: Physics
Specialties:
  • Condensed Matter Physics - Theory
  • High-Energy Physics - Theory
  • Quantum Physics
Approach: Theoretical

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 exploit the factorization of the initial state in terms of a massive and massless modes which emerges in the low energy limit, 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 contri- bution 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.

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Submission scipost_202103_00028v1 on 28 March 2021

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