Environment induced pre-thermalization 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 which constantly monitors the particle numbers ${\hat{n}}_{\mu }^{\uparrow }$ and ${\hat{n}}_{\mu }^{\downarrow }$ for each lattice site $\mu$. As expected, the environment induces an imaginary part $\gamma$ (i.e., decay rate) of the quasi-particle frequencies ${\omega }_{\mathbf{k}}\to {\omega }_{\mathbf{k}}-i\gamma$ and tends to diminish the correlations between lattice sites. Surprisingly, the environment does also steer the state of the system on intermediate time scales $\mathcal{O}(1/\gamma )$ to a pre-thermalized state very similar to a quantum quench (i.e., suddenly switching on the hopping rate $J$). Full thermalization occurs via local on-site heating and takes much longer.

6 pages, 4 figures

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• Environment-induced decay dynamics of anti-ferromagnetic order in Mott-Hubbard systems
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• Hierarchy of double-time correlations
• Quasi-particle propagation across semiconductor-Mott insulator interfaces
• Attraction versus repulsion between doublons or holons in Mott-Hubbard systems
• Effective time-dependent temperature for fermionic master equations beyond the Markov and the secular approximations
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• Bound States at Semiconductor -- Mott Insulator Interfaces