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arXiv:2112.00685 · Physical review. B./Physical review. B

Photoexcitations in the Hubbard model: Generalized Loschmidt amplitude analysis of impact ionization in small clusters

Clemens Watzenböck, Markus Wallerberger, Laurenz Ruzicka, Paul Worm, Karsten Held, Anna Kauch

Published Aug 26, 2022• 5 citations
arXivHTMLPDF

Abstract

We study photoexcitations in small Hubbard clusters of up to 12 sites. After the electric field pulse some of these clusters show an increase of the double occupation through impact ionization. We treat the time-dependent electromagnetic field classically and calculate time evolution by exact diagonalization. As a tool for better analyzing the out-of-equilibrium dynamics, we generalize the Loschmidt amplitude. In this way we are able to resolve which many-body energy eigenstates are responsible for impact ionization and which ones show pronounced changes in the double occupation and spin energy. Our analysis reveals that the increase of spin energy is of little importance for impact ionization. We further demonstrate that, for one-dimensional chains, the optical conductivity has a characteristic peak structure originating solely from vertex corrections.

DOI
10.1103/physrevb.106.085135

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We study photoexcitations in small Hubbard clusters of up to 12 sites. After the electric field pulse some of these clusters show an increase of the double occupation through impact ionization. We treat the time-dependent electromagnetic field classically and calculate time evolution by exact diagonalization. As a tool for better analyzing the out-of-equilibrium dynamics, we generalize the Loschmidt amplitude. In this way we are able to resolve which many-body energy eigenstates are responsible for impact ionization and which ones show pronounced changes in the double occupation and spin energy. Our analysis reveals that the increase of spin energy is of little importance for impact ionization. We further demonstrate that, for one-dimensional chains, the optical conductivity has a characteristic peak structure originating solely from vertex corrections.
We study the nonequilibrium response of a $4\ifmmode\times\else\texttimes\fi{}3$ Hubbard model at U=8U=8U=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 (multiexciton 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 onsite 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 disorder and geometric frustration of a triangular lattice.
Using the time-dependent Lanczos method, we study the nonequilibrium dynamics of the half-filled one-dimensional ionic Hubbard model, deep within the Mott insulating regime, under the influence of a transient laser pulse. In equilibrium, increasing the staggered potential in the Mott regime reduces the Mott gap and broadens the Hubbard bands, creating favorable conditions for impact ionization. After laser excitation, impact ionization is observed, with its occurrence depending on both the staggered potential and the laser pump frequency. By analyzing the time evolution of the kinetic, ionic, and Coulomb interaction energies, we identify a novel mechanism for impact ionization, in which excess ionic potential energy is converted into additional double occupancy-distinct from the conventional mechanism where excess kinetic energy drives this process. We further reveal that impact ionization arises from interference between excited states driven by photon excitations of the same order. These results present a new pathway for realizing impact ionization in strongly correlated electron systems.
Abstract Motivated by the recent progress in time-resolved nonequilibrium spectroscopy in condensed matter, we study an optically excited one-dimensional ionic Hubbard model by exact diagonalization. The model is relevant to organic crystals, transition metal oxides, or ultracold atoms in optical lattices. We implement numerical pump-probe measurements to calculate time-dependent conductivity and single-particle spectral functions. In general, short optical excitation induces a metallic behavior imprinted as a Drude peak in conductivity or an in-gap density of states. In a Mott insulator, we find that the induced Drude peak oscillates at the pump frequency and its second harmonic. The former comes from the oscillation of currents, and the latter from the interference of single- and three-photon excited states. In a band insulator, the Drude peak oscillates only at the pump frequency, and quantities such as the double occupancy do not oscillate. The absence of the second harmonic oscillation is due to the degeneracy of multi-photon excited states. The in-gap density of states in both insulators correlates with the Drude weight and the energy absorption for weak pumping. Strong pumping leads to saturation of the in-gap density of states and to suppression of the Drude weight in the Mott regime. We have also checked that the above features are robust for insulators in the intermediate parameter range. Our study demonstrates the distinct natures of the multi-photon excited states in two different insulators.
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.
The nonequilibrium Green's functions (NEGF) method has proven to be a powerful tool to describe quantum behavior for a variety of correlated many-body systems out of equilibrium. The cover image shows results of NEGF calculations of the response of a correlated chain of electrons in a Hubbard lattice to the impact of charged particles. The ions produce a local increase of the double occupation at the impact point, that is spreading through the system. With each successive particle impact the double-occupation level is significantly increased in time and gives rise to stable, delocalized doublons–bound electron pairs. For more details see article no. 1800490 by Michael Bonitz et al. within the special section “Non-Equilibrium Green's Functions”, guest-edited by Gianluca Stefanucci, Andrea Marini, and Stefano Bellucci (cf. also the Preface, article no. 1900335).