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arXiv:2007.16035 · Physical review. B./Physical review. B

Enhancement of impact ionization in Hubbard clusters by disorder and next-nearest-neighbor hopping

Anna Kauch, Paul Worm, Paul Prauhart, Michael Innerberger, Clemens Watzenböck, Karsten Held

Published Dec 16, 2020• 14 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.102.245125

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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.
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 present an exact diagonalization study of the self-energy of the two-dimensional Hubbard model. To increase the range of available cluster sizes we use a corrected ttt-JJJ model to compute approximate Green's functions for the Hubbard model. This allows to obtain spectra for clusters with 18 and 20 sites. The self-energy has several ``bands'' of poles with strong dispersion and extended incoherent continua with kkk-dependent intensity. We fit the self-energy by a minimal model and use this to extrapolate the cluster results to the infinite lattice. The resulting Fermi surface shows a transition from hole pockets in the underdoped regime to a large Fermi surface in the overdoped regime. We demonstrate that hole pockets can be completely consistent with the Luttinger theorem. Introduction of next-nearest-neighbor hopping changes the self-energy strongly and the spectral function with nonvanishing next-nearest-neighbor hopping in the underdoped region is in good agreement with angle-resolved photoelectron spectroscopy in the cuprates.
We present momentum-resolved single-particle spectra for the three-dimensional Hubbard model for the paramagnetic and antiferromagnetically ordered phase obtained within the dynamical cluster approximation. The effective cluster problem is solved by continuous-time quantum Monte Carlo simulations. The absence of a time discretization error and the ability to perform Monte Carlo measurements directly in Matsubara frequencies enable us to analytically continue the self-energies by maximum entropy, which is essential to obtaining momentum-resolved spectral functions for the N\'eel state. We investigate the dependence on temperature and interaction strength and the effect of magnetic frustration introduced by a next-nearest-neighbor hopping. One particular question we address here is the influence of the frustrating interaction on the metal-insulator transition of the three-dimensional Hubbard model.
Ferromagnetism in the one-dimensional Hubbard model with the next-nearest-neighbor hopping is explored by using the exact-diagonalization method in a small cluster and the equation-of-motion method in the thermodynamic limit with electron density n = 3/2. With these two complementary methods, it is found that an intermediate value of the next-nearest-neighbor hopping amplitude t1 tends to stabilize the fully polarized ferromagnetic state under the condition that the on-site coulomb interaction U is sufficiently large in our model. The ground-state phase diagram of the model is presented in the t1—U plane.