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

TL;DR

This paper analyzes the non-equilibrium dynamics of two coupled Tomonaga-Luttinger Liquids after a quantum quench using conformal field theory, revealing how correlation functions decay via exponential or power-law depending on the mode.

Contribution

It introduces a conformal field theory approach to study quenches in coupled TLLs, accounting for massive and massless modes and their impact on correlation decay.

Findings

Correlation functions factorize into multipoint functions at different times.

Decay behavior is exponential for massive mode, power-law for massless mode.

Applicable to models like Hubbard, Gaudin-Yang, and cold atom systems.

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.