Quantum quench dynamics of the Luttinger model

TL;DR

This paper investigates the non-equilibrium dynamics of the Luttinger model after a quantum quench, revealing how correlations evolve and are described by a generalized Gibbs ensemble, with implications for understanding thermalization in quantum systems.

Contribution

It provides detailed calculations of correlation functions post-quench and demonstrates the applicability of a generalized Gibbs ensemble to describe the system's long-term behavior.

Findings

Correlations decay and differ from equilibrium exponents after a quench.

Equal-time correlations follow power-law decay with modified exponents.

Generalized Gibbs ensemble accurately describes the long-time correlations.

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.