Relaxation dynamics of an exactly solvable electron-phonon model

TL;DR

This paper investigates the relaxation behavior of an exactly solvable electron-phonon model, demonstrating that stationary states can be described by a generalized Gibbs ensemble, especially using eigenmode occupancy operators.

Contribution

It introduces an exactly solvable electron-phonon model and shows how stationary states are described by a generalized Gibbs ensemble using eigenmode occupancy operators.

Findings

Expectation values relax to stationary values described by a generalized Gibbs ensemble.

Different initial conditions lead to distinct relaxation dynamics.

Eigenmode occupancy operators are key to constructing the stationary density matrix.

Abstract

We address the question whether observables of an exactly solvable model of electrons coupled to (optical) phonons relax into large time stationary state values and investigate if the asymptotic expectation values can be computed using a stationary density matrix. Two initial nonequilibrium situations are considered. A sudden quench of the electron-phonon coupling, starting from the noninteracting canonical equilibrium at temperature T in the electron as well as in the phonon subsystems, leads to a rather simple dynamics. A richer time evolution emerges if the initial state is taken as the product of the phonon vacuum and the filled Fermi sea supplemented by a highly excited additional electron. Our model has a natural set of constants of motion, with as many elements as degrees of freedom. In accordance with earlier studies of such type of models we find that expectation values which become stationary can be described by the density matrix of a generalized Gibbs ensemble which differs from that of a canonical ensemble. For the model at hand it appears to be evident that the eigenmode occupancy operators should be used in the construction of the stationary density matrix.