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Quenches in initially coupled Tomonaga-Luttinger Liquids: a conformal field theory approach
Statistical Mechanics · Submitted 16 Mar 2021
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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.
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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | 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. | contribution 1.00 | 0.93 | 0.09 | asserted 0.98 |
| s1 | 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. | method 0.95 | 0.89 | 0.05 | asserted 1.00 |
| s2 | In this way, we compute several correlation functions, which at leading order factorize into multipoint functions evaluated at different times for the two modes. | result 0.77 | 0.94 | 0.11 | asserted 1.00 |
| s3 | 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. | result 0.88 | 0.89 | 0.39 | asserted 0.85 |
| s4 | 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. | interpretation 0.96 | 0.69 | 0.18 | asserted 1.00 |
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Original 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.
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In summary, because of its intrinsic difficulty, the non-equilibrium dynamics of the one-dimensional Hubbard model have so far been investigated mainly by numerical or approximate means, see e.g. Refs. [ref] .
Real-Time Evolution in the Hubbard Model with Infinite Repulsion · Introduction · 0.93
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