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

Abstract

We present a straightforward implementation scheme for solving the time-dependent Schrödinger equation for systems described by the Hubbard Hamiltonian with time-dependent hoppings. The computations can be performed for clusters of up to 14 sites with, in principle, general geometry. For the time evolution, we use the exponential midpoint rule, where the exponentials are computed via a Krylov subspace method, which only uses matrix-vector multiplication. The presented implementation uses standard libraries for constructing sparse matrices and for linear algebra. Therefore, the approach is easy to use on both desktop computers and computational clusters. We apply the method to calculate time evolution of double occupation and nonequilibrium spectral function of a photo-excited Mott-insulator. The results show that not only the double occupation increases due to creation of electron-hole pairs but also the Mott gap becomes partially filled.

Photoexcitations in the Hubbard model -- generalized Loschmidt amplitude analysis of impact ionization in small clusters

“…Impact ionization is a genuine non-equilibrium process, which is particularly challenging to describe in theory if electronic correlations are strong, so that weak coupling perturbation theory [3] or the Boltzmann equation [12] cannot be reliably applied. One possibility is to employ nonequilibrium dynamical mean-field theory [6,7,14] which treats local correlations non-perturbatively, another route is to study the time evolution directly for small clusters [10,11,15,16]. In Refs.…”