Finite time interaction quench in a Luttinger model

Abstract

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.

8 pages, 4 figures; updated version; to appear in Phys. Rev. B

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• Finite-time quantum quenches in the XXZ Heisenberg chain
• From Luttinger liquids to Luttinger droplets via higher-order bosonization identities
• Non-equilibrium dynamics of an ultracold Bose gas under a multi-pulsed quantum quench in interaction
• Entanglement entropy of a three-spin interacting spin chain with a time-reversal breaking impurity at one boundary
• Chiral Instabilities in Driven-Dissipative Quantum Liquids