  Based on the framework of Kubo formulism, we develop the minimally entangled
typical thermal state algorithm to study the temperature and time dependence of
current-current correlation function in one-dimensional spinless fermion model,
taking into account both the electron-electron (e-e) intersite interaction and
the dynamic disorder induced by classical phonons. Without e-e interaction, the
numerical results, showing an exponential decay of the time dependent
correlation, could be precisely compared with that from the analytical
derivation, namely, from the generalized Langevin equation. More importantly,
when a strong enough e-e interaction is presence, we find a long-time
correlation in the regime of small dynamic disorder, indicating the breakdown
of thermal relaxation, which is a typical many-body effect. On the basis of
this finding, we show that it might be applied to understand the metalliclike
charge transport and the abnormal improvement of the conductivity with respect
to the redoping experiment in K$_3$C$_{60}$, an organic superconducting
material.
