Efficient Magnus-type integrators for solar energy conversion in Hubbard models

Abstract

Strongly interacting electrons in solids are generically described by Hubbardtype models, and the impact of solar light can be modeled by an additional time-dependence. This yields a finite dimensional system of ordinary differential equations (ODE)s of Schrödinger type, which can be solved numerically by exponential time integrators of Magnus type. The efficiency may be enhanced by combining these with operator splittings. We will discuss several different approaches of employing exponential-based methods in conjunction with an adaptive Lanczos method for the evaluation of matrix exponentials and compare their accuracy and efficiency. For each integrator, we use defect-based local error estimators to enable adaptive time-stepping. This serves to reliably control the approximation error and reduce the computational effort

References in corpus (15)

• The Magnus expansion and some of its applications
• Nonequilibrium dynamical mean-field theory and its applications
• Nonequilibrium dynamical mean-field theory
• A Krylov subspace algorithm for evaluating the phi-functions appearing in exponential integrators
• Oxide Heterostructures for Efficient Solar Cells
• High-order commutator-free exponential time-propagation of driven quantum systems
• Role of impact ionization in the thermalization of photo-excited Mott insulators
• Photovoltaic effect for narrow-gap Mott insulators
• Numerical time propagation of quantum systems in radiation fields
• Impact ionization processes in the steady state of a driven Mott insulating layer coupled to metallic leads
• Introduction to Hubbard Model and Exact Diagonalization
• Electron-light interaction in nonequilibrium -- exact diagonalization for time dependent Hubbard Hamiltonians
• Computable upper error bounds for Krylov approximations to matrix exponentials and associated $\phi$-functions
• Sixth-order schemes for laser--matter interaction in Schrödinger equation
• Order conditions for exponential integrators

Cited by in corpus (5)

• Enhancement of impact ionization in Hubbard clusters by disorder and next-nearest-neighbor hopping
• Electron-light interaction in nonequilibrium -- exact diagonalization for time dependent Hubbard Hamiltonians
• Photoexcitations in the Hubbard model -- generalized Loschmidt amplitude analysis of impact ionization in small clusters
• Quantum simulation of time-dependent Hamiltonians via commutator-free quasi-Magnus operators
• Commutator-free Cayley methods