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

Abstract

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 computer and computational cluster. 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 occupancy increases due to creation of electron-hole pairs but also the Mott gap becomes partially filled.

arXiv comment21 pages, 12 figures

References in corpus (20)

• The density-matrix renormalization group in the age of matrix product states
• Nonequilibrium dynamical mean-field theory and its applications
• Nonlinear lattice dynamics as a basis for enhanced superconductivity in YBa2Cu3O6.5
• High-order commutator-free exponential time-propagation of driven quantum systems
• Photoinduced $\eta$ Pairing in the Hubbard Model
• Photo-induced states in a Mott insulator
• Ultra-fast photo-carrier relaxation in Mott insulators with short-range spin correlations
• Role of impact ionization in the thermalization of photo-excited Mott insulators
• Dynamics of screening in photo-doped Mott insulators
• Multi-band non-equilibrium GW+EDMFT formalism for correlated insulators
• Photovoltaic effect for narrow-gap Mott insulators
• Producing Coherent Excitations in Pumped Mott Antiferromagnetic Insulators
• Light-Enhanced Spin Fluctuations and d-Wave Superconductivity at a Phase Boundary
• Quantum Boltzmann equation for strongly correlated systems: comparison to dynamical mean field theory
• Numerical time propagation of quantum systems in radiation fields
• Pseudogap Anderson impurity model out of equilibrium: A master equation tensor network approach
• Effective doublon and hole temperatures in the photo-doped dynamic Hubbard model
• Time-dependent spectral properties of photoexcited one-dimensional ionic Hubbard model: an exact diagonalization study
• Effects of frustration on the nonequilibrium dynamics of photo-excited lattice systems
• Efficient Magnus-type integrators for solar energy conversion in Hubbard models

Cited by in corpus (12)

• Fluctuating Nature of Light-Enhanced $d$-Wave Superconductivity: A Time-Dependent Variational Non-Gaussian Exact Diagonalization Study
• Enhancement of impact ionization in Hubbard clusters by disorder and next-nearest-neighbor hopping
• Impact ionization and multiple photon absorptions in the two-dimensional photoexcited Hubbard model
• Photoexcitations in the Hubbard model -- generalized Loschmidt amplitude analysis of impact ionization in small clusters
• Site-selective doublon-holon dynamics in a pumped one-dimensional Hubbard superlattice with staggered Coulomb interactions
• Trie-based ranking of quantum many-body states
• Efficient Magnus-type integrators for solar energy conversion in Hubbard models
• A new pathway to impact ionization in a photo-excited one-dimensional ionic Hubbard model
• Quench dynamics in the one-dimensional mass-imbalanced ionic Hubbard model
• Nonclassical dynamics of Néel vector and magnetization accompanied by THz and high-harmonic radiation from ultrafast-light-driven NiO antiferromagnet insulator
• Photoinduced melting dynamics and collective mode in a correlated charge-ordered system
• Laser-Induced Commensurate-Incommensurate Transition of Charge Order in a Hubbard Superlattice