Finite time interaction quench in a Luttinger model

We analyze the dynamics of a Luttinger model 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, b...

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Bibliographic Details
Published in:arXiv.org 2014-06
Main Authors: Sachdeva, Rashi, Nag, Tanay, Agarwal, Amit, Dutta, Amit
Format: Article
Language:English
Subjects:
Mathematical models
Perturbation methods
Scaling
Online Access:Get full text
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Summary:We analyze the dynamics of a Luttinger model 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, a.) the Loschmidt echo for a finite quench duration \(\tau\), 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.
ISSN:2331-8422
DOI:10.48550/arxiv.1311.1926