2013/11/30 by Rashi Sachdeva, Tanay Nag, Amit Agarwal +1 · 1 citation
Mathematics · Physics and Astronomy · #Adiabatic process #Condensed matter physics #Context (archaeology) #Electron #Limiting #Luttinger liquid #Mathematical physics #Mathematics #Perturbation theory (quantum mechanics) #Physics #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Quantum electrodynamics #Quantum many-body systems #Quantum mechanics #Scaling #Statistical physics #cond-mat.mes-hall #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevb.90.045421
published as Phys. Rev. B 90, 045421 (2014) · 8 pages, 4 figures; updated version; to appear in Phys. Rev. B
arxiv created 2014/06/28 · openalex publication_date 2014/07/23 · arxiv updated 2014/08/27 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 \ensuremathτ. 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 strength as a small parameter, for all \ensuremathτ. We derive the corrections appearing in (a) the Loschmidt echo for a finite quench duration \ensuremathτ, (b) the scaling of the echo following a sudden (\ensuremathτ\ensuremath→0) quench, and (c) the scaling of the echo after an adiabatic (\ensuremathτ\ensuremath→\ensuremath∞) quench. We study in detail the limiting cases of the echo in the early-time and infinite-time limits, 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.