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

TL;DR

This paper introduces an efficient numerical method for solving the time-dependent Hubbard model, enabling simulations of electron-light interactions in nonequilibrium states with up to 14 sites, revealing dynamics of double occupation and spectral functions.

Contribution

The paper presents a straightforward implementation of time evolution for Hubbard Hamiltonians with time-dependent hoppings using Krylov subspace methods, suitable for larger clusters and general geometries.

Findings

Double occupation increases after photo-excitation.

Mott gap becomes partially filled in nonequilibrium.

Method enables detailed study of electron-light interactions.

Abstract

We present a straightforward implementation scheme for solving the time dependent Schr\"odinger 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 computer and computational cluster. 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 occupancy increases due to creation of electron-hole pairs but also the Mott gap becomes partially filled.