Marginal quenches and drives in Tomonaga-Luttinger liquids

TL;DR

This paper investigates the non-equilibrium dynamics of Tomonaga-Luttinger liquids under marginal deformations, providing exact analytical results for quenches and periodic drives, and exploring their stability, revivals, and thermal properties.

Contribution

It offers the first exact analytical analysis of quench and drive dynamics in marginally deformed Tomonaga-Luttinger liquids, linking these to conformal field theory and string theory interpretations.

Findings

Revivals and orthogonalities in quench dynamics.

Stability or instability depending on drive parameters.

Dependence of dynamics on the ratio of Luttinger parameters.

Abstract

We study Tomonaga-Luttinger liquids thrown out of equilibrium by marginal deformations in the form of interaction modulations. This is modeled by quenching or periodically driving the Luttinger parameter or, equivalently, the compactification radius of the free boson conformal field theory between two different values. We obtain exact analytical results for the evolution of the Loschmidt echo and observables such as the particle and energy densities. Starting from generic initial states, the quench dynamics are shown to exhibit revivals and temporal orthogonalities. For the periodic drive, we show stability or instability of time-evolved physical quantities dependent on the drive parameters. We also compare the corresponding marginally deformed thermal density matrices by non-perturbatively evaluating their R\'{e}nyi divergence as a Euclidean quench. All the dynamics are shown to be crucially dependent on the ratio of the Luttinger parameters, which corresponds to the Zamolodchikov distance in the space of marginal deformations. Our setup is equivalently interpreted as the dynamics of the bosonic string upon instantaneous changes of the target-space radius.