Marginal quenches and drives in Tomonaga-Luttinger liquids

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 Rényi 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.

64 pages, LaTeX, 12 figures; minor updates and typos corrected; final published version

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Cited by in corpus (7)

• Quantum information geometry of driven CFTs
• Holographic Quantum Scars
• Inhomogeneous quenches as state preparation in two-dimensional conformal field theories
• Exact Dirac-Bogoliubov-de Gennes Dynamics for Inhomogeneous Quantum Liquids
• Exact Dynamics and Shortcuts to Adiabaticity in the Tomonaga-Luttinger Liquid
• Transitionless Quantum Driving of the Tomonaga-Luttinger Liquid
• Chiral Instabilities in Driven-Dissipative Quantum Liquids