We study the non-equilibrium response of a 4x3 Hubbard model at U=8 under the influence of a short electric field pulse, with the main focus on multiple photon excitations and on the change of double occupancy after the pulse. The behavior mainly depends on the driving frequency of the electric field. The largest change of double occupancy occurs during the pulse. For frequencies below the Mott gap, we observe multiphoton excitations at large field intensities. For frequencies beyond the gap energy, there is a region where Auger recombination reduces the double occupancy after the pulse. Impact ionization (Multi Exciton Generation), namely a growing double occupancy after the pulse, occurs for frequencies larger than twice the Mott gap. From the Loschmidt amplitude we compute the eigenstate spectrum of the quantum state after the pulse, observing multiple distinct photon excitation peaks, in line with expectations from a quasiparticle picture. We introduce a technique with which we analyze the time evolution of double occupancy in each peak individually. The long-term behavior of the double occupancy almost only depends on the absorbed energy, and we explore the connection of this property to the Eigenstate Thermalization Hypothesis.
We perform time-resolved exact diagonalization of the Hubbard model with time dependent hoppings on small clusters of up to $12$ sites. Here, the time dependence originates from a classic electromagnetic pulse, which mimics the impact of a photon. We investigate the behavior of the double occupation and spectral function after the pulse for different cluster geometries and on-site potentials. We find impact ionization in all studied geometries except for one-dimensional chains. Adding next-nearest neighbor hopping to the model leads to a significant enhancement of impact ionization, as does di…
Phase Transition in a One-Dimensional Extended Peierls-Hubbard Model with a Pulse of Oscillating Electric Field: III. Interference Caused by a Double Pulse
We study photoexcitations in small Hubbard clusters of up to 12 sites, some of which show an increase of the double occupation after the electric field pulse through impact ionization. Here, the time-dependent electromagnetic field is introduced through a Peierls substitution and the time evolution is calculated by exact diagonalization with commutator-free Magnus integrators. As a tool to better analyze the out-of-equilibrium dynamics, we generalize the Loschmidt amplitude. This way, we are able to resolve which many-body energy eigenstates are responsible for impact ionization and which show…
Motivated by the recent development of time-resolved resonant-inelastic x-ray scattering (TRRIXS) in photoexcited antiferromagnetic Mott insulators, we numerically investigate momentum-dependent transient spin dynamics in a half-filled Hubbard model on a square lattice. After turning off a pumping photon pulse, the intensity of a dynamical spin structure factor temporally oscillates with frequencies determined by the energy of two magnons in the antiferromagnetic Mott insulator. We find an antiphase behavior in the oscillations between two orthogonal momentum directions, parallel and perpendic…
The photoexcitation of a Mott insulator on a square lattice weakens the intensity of both single- and two-magnon excitations as observed in time-resolved resonant-inelastic X-ray scattering and time-resolved Raman scattering, respectively. However, the spectral changes in the low-energy regions below the magnons have not yet been clearly understood. To uncover the nature of the photoinduced low-energy magnetic excitations of the Mott insulator, we numerically investigate the transient magnetic dynamics in a photoexcited half-filled Hubbard model on a square lattice. After turning off a pump pu…
Phase Transition in a One-Dimensional Extended Peierls-Hubbard Model with a Pulse of Oscillating Electric Field: II. Linear Behavior in Neutral-to-Ionic Transition
Phase Transition in a One-Dimensional Extended Peierls-Hubbard Model with a Pulse of Oscillating Electric Field: I. Threshold Behavior in Ionic-to-Neutral Transition
We compute scattering rates for electrons in the two-dimensional Hubbard model for a one-orbital metal and a two-orbital band insulator by means of the Boltzmann scattering equation (BSE) and dynamical mean-field theory (DMFT). As an intermediate method between both, we also consider the BSE without momentum conservation. In the weak interaction regime and for the band insulator, the last two agree to very good accuracy. The BSE with momentum conservation, on the other hand, shows slightly larger scattering rates, and a momentum differentiation of these on the Fermi surface. For the Mott insul…
