# Finite-time interaction quench in a Luttinger liquid

Sachdeva, Rashi ; Nag, Tanay ; Agarwal, Amit ; Dutta, Amit (2014) Finite-time interaction quench in a Luttinger liquid Physical Review B, 90 (4). ISSN 1098-0121

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Official URL: http://doi.org/10.1103/PhysRevB.90.045421

Related URL: http://dx.doi.org/10.1103/PhysRevB.90.045421

## Abstract

We analyze the dynamics of a Luttinger liquid following a quench in the electron-electron interaction strength, where the change in the interaction strength occurs over a finite time scale $\tau$. We study the Loschmidt echo (the overlap between the initial and final state) as a function of time, both numerically and within a perturbation scheme, treating the change in the interaction as a small parameter, for all $\tau$. We derive the corrections appearing in the a.) Loschmidt echo for a finite $\tau$, b.) the scaling of the echo following a sudden ($\tau \to 0$) quench, and c.) the scaling of the echo after an adiabatic ($\tau \to \infty$) quench. We study in detail, the limiting cases of the echo in the early time and infinite time limit, and provide scaling arguments to understand these in a general context. We also show that our perturbative results are in good agreement with the exact numerical ones.

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