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

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Computational Chemistry

Background:

• The Hubbard Hamiltonian is crucial for understanding strongly correlated electron systems.
• Simulating time-dependent phenomena in these systems is computationally challenging.
• Accurate modeling of photo-excited states is vital for materials science.

Purpose of the Study:

• To present a straightforward and efficient implementation for solving the time-dependent Schrödinger equation.
• To enable simulations of systems with time-dependent hoppings up to 14 sites.
• To investigate the behavior of photo-excited Mott-insulators.

Main Methods:

• Utilized the exponential midpoint rule for time evolution.
• Employed Krylov subspace methods for computing matrix exponentials via matrix-vector multiplication.
• Leveraged standard sparse matrix and linear algebra libraries for implementation.

Main Results:

• Successfully simulated time evolution of double occupation and nonequilibrium spectral functions.
• Observed an increase in double occupation due to electron-hole pair creation.
• Found partial filling of the Mott gap in photo-excited Mott-insulators.

Conclusions:

• The developed method is computationally efficient and accessible on standard hardware.
• The simulation provides new insights into the dynamics of photo-excited Mott-insulators.
• The approach is applicable to general geometries and systems up to 14 sites.