Quench dynamics in low-dimensional quantum models of many body systems

I will describe nonequilibrium dynamics  in interacting quantum systems

mainly  using the protocol of quenching the systems and following their evolution in

time. I'll discuss the evolution  Lieb-Liniger system, a gas of interacting bosons

moving on the continuous infinite line and interacting via a short range potential.

Considering first a finite number of bosons on the line  we find that for any value of

repulsive coupling  the system asymptotes towards a strongly repulsive gas for any

initial state, while for an attractive coupling, the system forms a maximal bound

state that dominates at longer times. In either case the system equilibrates but does

not thermalize, an effect that is consistent with prethermalization.  Then

considering the system in the thermodynamic limit - with the number of bosons and

the system size sent to infinity at a constant density  and  the long time limit taken

subsequently-  I'll discuss the equilibration of the density and density-density

correlation functions for strong but finite positive coupling and show they are

described by  GGE (generalized Gibbs ensemble) for translationally invariant initial

states with short  range correlations. If the initial state is strongly non translational

invariant the system does not equilibrate.  I will give some examples of quenches:

from a Mott insulator initial state or from a domain wall configuration or a Newton’s

Cradle.   I also will show that if the coupling constant is negative the GGE fails for

most initial states in the Lieb-Liniger model. If time permits I shall discuss also the

quench dynamics of the XXZ Heisenberg chain.