Environment-induced prerelaxation in the Mott-Hubbard model

Abstract

Via the hierarchy of correlations, we study the strongly interacting Fermi-Hubbard model in the Mott insulator state and couple it to a Markovian environment that constantly monitors the particle numbers ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n}}_{\ensuremath{\mu}}^{\ensuremath{\uparrow}}$ and ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n}}_{\ensuremath{\mu}}^{\ensuremath{\downarrow}}$ for each lattice site $\ensuremath{\mu}$. As expected, the environment induces an imaginary part $\ensuremath{\gamma}$ (i.e., the decay rate) of the quasiparticle frequencies ${\ensuremath{\omega}}_{\mathbf{k}}\ensuremath{\rightarrow}{\ensuremath{\omega}}_{\mathbf{k}}\ensuremath{-}i\ensuremath{\gamma}$, and it tends to diminish the correlations between lattice sites. Surprisingly, the environment also steers the state of the system on intermediate timescales $O(1/\ensuremath{\gamma})$ to a prerelaxed state very similar to the prethermalized state after a quantum quench (i.e., suddenly switching on the hopping rate $J$). Full relaxation or thermalization occurs via local on-site heating and takes much longer.