Prethermalization and thermalization of a quenched interacting Luttinger liquid

Michael Buchhold, Markus Heyl, and Sebastian Diehl
Phys. Rev. A 94, 013601 – Published 8 July 2016

Abstract

We study the relaxation dynamics of interacting one-dimensional fermions with band curvature after a weak quench in the interaction parameter at zero temperature. Our model lies within the class of interacting Luttinger liquids, where the harmonic Luttinger theory is extended by a weak-integrability-breaking phonon scattering term. In order to solve for the nonequilibrium time evolution, we use quantum kinetic equations exploiting the resonant but subleading character of the phonon interaction term. The interplay between phonon scattering and the quadratic Luttinger theory leads to the emergence of three distinct spatiotemporal regimes for the fermionic real-space correlation function. It features the crossover from a prequench to a prethermal state, finally evolving towards a thermal state on increasing length and time scales. The characteristic algebraically decaying real-space correlations in the prethermalized regime become modulated by an amplitude that is decaying in time according to a stretched exponential as an effect of the interactions. The asymptotic thermalization dynamics is governed by energy transport over large distances from the thermalized to the nonthermalized regions via macroscopic, dynamical slow modes. This is revealed in an algebraic decay of the system's effective temperature. The numerical value of the associated exponent agrees with the dynamical critical exponent of the Kardar-Parisi-Zhang universality class. We also discuss a criterion for the applicability of this theory away from the integrable limit of noninteracting fermions.

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  • Received 23 May 2016

DOI:https://doi.org/10.1103/PhysRevA.94.013601

©2016 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
  1. Physical Systems
Atomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Michael Buchhold1, Markus Heyl2, and Sebastian Diehl1

  • 1Institut für Theoretische Physik, Universität zu Köln, D-50937 Cologne, Germany
  • 2Physik Department, Technische Universität München, 85747 Garching, Germany

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Issue

Vol. 94, Iss. 1 — July 2016

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