Electron-light interaction in nonequilibrium: exact diagonalization for time-dependent Hubbard Hamiltonians
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Electron-light interaction in nonequilibrium: exact diagonalization for time-dependent Hubbard Hamiltonians Michael Innerberger1, Paul Worm2 , Paul Prauhart2 , Anna Kauch2,a 1 Institute of Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstr. 8-10,
1040 Wien, Austria
2 Institute of Solid State Physics, Vienna University of Technology, Wiedner Hauptstr. 8-10, 1040 Wien,
Austria Received: 5 June 2020 / Accepted: 4 November 2020 © The Author(s) 2020
Abstract We present a straightforward implementation scheme for solving the timedependent 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.
1 Introduction Photo-induced states of matter gain increasing attention for their exotic properties [1–6] and possible applications, e.g., in the context of energy conversion [7,8]. The description of these states necessitates nonequilibrium approaches, which are particularly demanding in cases where light brings a strongly correlated electronic system out of equilibrium. The approximate theoretical approaches to correlated systems are being successfully adapted to treat systems out of equilibrium (e.g., nonequilibrium dynamical mean-field theory (DMFT) [9], dynamical cluster approximation [10], auxiliary master equation approach [11], GW [12]). The numerically exact approaches, exact diagonalization (ED) [13], or density-matrix renormalization group [5,14], where the error can be systematically controlled, are still limited to relatively small system sizes or short times [15]. They are, however, invaluable for benchmarking sophisticated approximate methods. The purpose of this paper is to present a straightforward implementation of the ED method using well-known data formats and algorithms in order to employ highly optimized libraries. The method currently allows for calculations with up to 14 sites.
a e-mail: [email protected] (corresponding author)
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Eur. Phys. J. Plus
(2020) 135:922
We specifically focus on the application of the method to calculate electronic properties of a system that is described by a time-dependent Hubbard Hamiltonian. The time dependence is introduced by coupling of the electronic system to a electromagnetic (EM)
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