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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: Thierry Giamarchi · Paola Ruggiero
Arxiv Link: (pdf)
Date accepted: 2021-08-10
Date submitted: 2021-07-05 22:30
Submitted by: Ruggiero, Paola
Submitted to: SciPost Physics
Academic field: Physics
  • Condensed Matter Physics - Theory
  • High-Energy Physics - Theory
  • Quantum Physics
Approach: Theoretical


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.

Published as SciPost Phys. 11, 055 (2021)

Author comments upon resubmission

Dear Editors,

We are submitting a revised version of the manuscript scipost_202103_00028v1
“Quenches in initially coupled Tomonaga-Luttinger Liquids: a conformal field theory approach”.

We would like to thank the editors for their work and the referees for
their useful comments and suggestions.

We believe that we thoroughly addressed all the comments of the referees
in the new version of the manuscript, and that the latter, in its present form, fully meets the criteria of Scipost Physics.
In particular, the inclusion of an entire new subsection of the Introduction where we discuss the motivations and the novelty of our approach should have answered the main criticism by both referee and clarified why and how our current results generalise considerably those already present in the literature.


Paola Ruggiero
Laura Foini
Pasquale Calabrese
Thierry Giamarchi

List of changes

- New subsection (Sec. 1.1) with goals and main results
- Extended discussion and justification of the class of initial states (Sec. 2 and Sec. 4)
- Typos corrected

Reports on this Submission

Anonymous Report 1 on 2021-7-19 (Invited Report)


I have read the authors reply and the new manuscript and I think that they have addressed carefully the main points of my report, in particular with the addition of the new Sec. 1.1 . I think in this form the manuscript deserves publication in SciPost.

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