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

• Published in: European physical journal plus 2020-11, Vol.135 (11), p.922-922, Article 922
• Main Authors: Innerberger, Michael, Worm, Paul, Prauhart, Paul, Kauch, Anna
• Format: Article
• Language: English
• Subjects: Applied and Technical Physics; Atomic; Boundary conditions; Clusters; Complex Systems; Condensed Matter Physics; Equilibrium; Evolution; Geometry; Hamiltonian functions; Hilbert space; Holes (electron deficiencies); Light; Linear algebra; Mathematical analysis; Mathematical and Computational Physics; Matrix algebra; Molecular; Multiplication; Onsite; Optical and Plasma Physics; Ordinary differential equations; Personal computers; Physics; Physics and Astronomy; Regular; Regular Article; Schrodinger equation; Sparse matrices; Subspace methods; Theoretical; Time dependence
• ISSN: 2190-5444; 2190-5444
• DOI: 10.1140/epjp/s13360-020-00919-2

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.