Breakdown of the Generalized Gibbs Ensemble for Current-Generating Quenches

We establish a relation between two hallmarks of integrable systems: the relaxation towards the generalized Gibbs ensemble (GGE) and the dissipationless charge transport. We show that the former one is possible only if the so-called Mazur bound on the charge stiffness is saturated by local conserved quantities. As an example we show how a non-GGE steady state with a current can be generated in the one-dimensional model of interacting spinless fermions with a flux quench. Moreover, an extended GGE involving the quasilocal conserved quantities can be formulated for this case.

Figure 1

Time dependence of $⟨J⟩$ and $4⟨J^{\prime }⟩$ after quenching the flux at $t=0$ for $L=26$ and $V=1$. (a) The system is initially in equilibrium microcanonical state with $\beta =0.35$ while after the quench it has effective $\beta =0.15$. (b) The system is in the ground state and the flux is quenched from ${\varphi }_0=\pi /2$ to 0.

Figure 2

a) $D^{\prime }/D$ vs $1/L$, where $D^{\prime }$ is the stiffness related with $J^{\prime }$. b) $⟨J⟩/⟨J^{\prime }⟩$ obtained for $\overline{\rho }$, Eq. (11), for $\beta \to 0$. Horizontal lines show analytical results. Exact diagonalization has been carried out for $V=1$ with $\varphi =\pi /L$ and $2\pi /L$ for even and odd $N$, respectively.