K-ETH Algorithm for calculating finte temperature Green's functions of strongly correlated systems.

We illustrate an efficient algorithm for calculating Fermionic many-body Green\^{a}\texteuro \texttrademark s functions at finite temperature, which avoid Gibbs state preparation techniques to initialize the calculation. Instead, by properly invoking the eigenstate thermalization hypothesis (ETH), we are able to initialize the computation rapidly. We show how sum rules guarantee the Green\^{a}\texteuro \texttrademark s functions are correct for short times and we also show how the time at which results begin to fail grows with the system size being simulated. We propose that this algorithm can have applicability to the simulations of a wide range of different strongly correlated systems.