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We present a straightforward implementation scheme for solving the timedependent Schr\"odinger equation for systems described by the HubbardHamiltonian with time dependent hoppings. The computations can be performed forclusters of up to 14 sites with in principle general geometry. For the timeevolution, we use the exponential midpoint rule, where the exponentials arecomputed via a Krylov subspace method, which only uses matrix-vectormultiplication. The presented implementation uses standard libraries forconstructing sparse matrices and for linear algebra therefore the approach iseasy to use on both desktop computer and computational cluster. We apply themethod to calculate time evolution of double occupation and nonequilibriumspectral function of a photo-excited Mott-insulator. The results show that notonly the double occupancy increases due to creation of electron-hole pairs butalso the Mott gap becomes partially filled.

Electron-light interaction in nonequilibrium -- exact diagonalization for time dependent Hubbard Hamiltonians