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.
Highlights
As mentioned in the introduction we are interested in studying the time evolution after a quench in which the post-quench low-energy physics is captured by two different TomonagaLuttinger liquids
In the rest of the paper we focus on the thermodynamic limit (TDL), namely infinite system size
This case has instead been considered in Ref. [34], where the quench dynamics of a Tomonaga-Luttinger Liquids (TLLs) after a sudden change of the TLL parameter, say from K0 to Kf, is studied via a Bogoliubov approach
Summary
In recent times the theoretical understanding of out-of-equilibrium homogeneous systems in 1D has become central in statistical and condensed matter physics, as counterpart to the enormous experimental advances brought by cold atoms [1, 2]. In addition to the practical possibility of finding ramps with the proper speed for the field theory to remain valid, the theoretical study of the non-equilibrium dynamics of these conformal systems has its per se interest and provides very fundamental qualitative features that are difficult to get by other means in such generality (e.g., the previously mentioned exponential and power-law decays of correlations). The study of the problem is, instead, much more complicated when no such obvious change of variable allows to reduce the problem to two decoupled modes, see for instance [105] In this direction, few recent studies investigated the quench dynamics in the tunnelling coupling of two TLLs with different sound velocity and/or Luttinger parameter [114,115,116], aiming at understanding the effect of such “imbalance” between them. How much the above results depend on the specific quench considered there is not clear
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