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

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 ev...

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Bibliographic Details
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
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Summary: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.
ISSN:2190-5444
2190-5444
DOI:10.1140/epjp/s13360-020-00919-2