Quantum quench dynamics of the Luttinger model

Abstract

The dynamics of the Luttinger model after a quantum quench is studied. We compute in detail one and two-point correlation functions for two types of quenches: from a non-interacting to an interacting Luttinger model and vice-versa. In the former case, the non-interacting Fermi gas features in the momentum distribution and other correlation functions are destroyed as time evolves. In the infinite-time limit, equal-time correlations are power-laws but the critical exponents are found to differ from their equilibrium values. In all cases, we find that these correlations are well described by a generalized Gibbs ensemble [M. Rigol et al., Phys. Rev. Lett. 98, 050405 (2007)], which assigns a momentum dependent temperature to each eigenmode.

16 pages, 3 figures

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• Optimal control for unitary preparation of many-body states: application to Luttinger liquids
• Relaxation dynamics of an exactly solvable electron-phonon model
• Universal Dephasing of Many-Body Rabi Oscillations of Atoms in One-Dimensional Traps
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