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Journal of the Physical Society of Japan

Low-lying Photoexcited States of a One-Dimensional Ionic Extended Hubbard Model

横井 浩太, Nobuya Maeshima, Ken-ichi Hino

Published Sep 22, 2017• 2 citations
Publisher

Abstract

We investigate the properties of low-lying photoexcited states of a one-dimensional (1D) ionic extended Hubbard model at half-filling. Numerical analysis by using the full and Lanczos diagonalization methods shows that, in the ionic phase, there exist low-lying photoexcited states below the charge transfer gap. As a result of comparison with numerical data for the 1D antiferromagnetic (AF) Heisenberg model, it was found that, for a small alternating potential Δ, these low-lying photoexcited states are spin excitations, which is consistent with a previous analytical study [Katsura et al., Phys. Rev. Lett. 103, 177402 (2009)]. As Δ increases, the spectral intensity of the 1D ionic extended Hubbard model rapidly deviates from that of the 1D AF Heisenberg model and it is clarified that this deviation is due to the neutral-ionic domain wall, an elementary excitation near the neutral-ionic transition point.

DOI
10.7566/jpsj.86.104708

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We investigate the properties of low-lying photoexcited states of a one-dimensional (1D) ionic extended Hubbard model at half-filling. Numerical analysis by using the full and Lanczos diagonalization methods shows that, in the ionic phase, there exist low-lying photoexcited states below the charge transfer gap. As a result of comparison with numerical data for the 1D antiferromagnetic (AF) Heisenberg model, it was found that, for a small alternating potential Δ, these low-lying photoexcited states are spin excitations, which is consistent with a previous analytical study [Katsura et al., Phys. Rev. Lett. 103, 177402 (2009)]. As Δ increases, the spectral intensity of the 1D ionic extended Hubbard model rapidly deviates from that of the 1D AF Heisenberg model and it is clarified that this deviation is due to the neutral-ionic domain wall, an elementary excitation near the neutral-ionic transition point.
We investigate the ground-state phase diagram of the one-dimensional 'ionic' Hubbard model with an alternating periodic potential at half-filling by numerical diagonalization of finite systems with the Lanczos and density matrix renormalization group methods. We identify an insulator–insulator phase transition from a band to a correlated insulator with simultaneous charge and bond-charge order. The transition point is characterized by the vanishing of the optical excitation gap while simultaneously the charge and spin gaps remain finite and equal. Indications for a possible second transition into a Mott-insulator phase are discussed.
Abstract Utilizing the time-dependent Lanczos method, we investigate the photoexcitation dynamics of the one-dimensional (1D) extended Peierls–Hubbard model at quarter filling. In equilibrium, it is well established that introducing the nearest-neighbour interaction V into the 1D Peierls–Hubbard model can lead to the formation of Mott–Hubbard excitons, which exhibit a characteristic frequency in the optical conductivity that is lower than the Mott gap. Ultrafast photoexcitation of this model gives rise to a transient metallic state for V < 2, characterized by several features, including a zero-frequency Drude peak in the post-pump optical conductivity, an increase in the density of charge carriers, and enhanced electron hopping between dimers. In contrast, when V ≥ 2, this metallic state is no longer observed, as photoinduced carriers bind to form excitons, thereby inhibiting metallic behavior. These results highlight a parallel between the optical excitation of the 1D extended Peierls–Hubbard model at quarter filling and that of the 1D extended Hubbard model at half filling, suggesting a universal mechanism governing their photoinduced responses.
Real-time dynamics of charge density and lattice displacements is studied during photoinduced ionic-to-neutral phase transitions by using a one-dimensional extended Peierls-Hubbard model with alternating potentials for the one-dimensional mixed-stack charge-transfer complex, TTF-CA. The time-dependent Schrödinger equation and the classical equation of motion are solved for the electronic and lattice parts, respectively. We show how neutral domains grow in the ionic background. As the photoexcitation becomes intense, more neutral domains are created. Above threshold intensity, the neutral phase is finally achieved. After the photoexcitation, ionic domains with wrong polarization also appear. They quickly reduce the averaged staggered lattice displacement, compared with the averaged ionicity. As the degree of initial lattice disorder increases, more solitons appear between these ionic domains with different polarizations, which obstruct the growth of neutral domains and slow down the transition.
We investigate the ground-state phase diagram of the one-dimensional half-filled Hubbard model with an alternating potential---a model for the charge-transfer organic materials and the ferroelectric perovskites. We numerically determine the global phase diagram of this model using the level-crossing and the phenomenological renormalization-group methods based on the exact diagonalization calculations. Our results support the mechanism of the double phase transitions between Mott and band insulators pointed out by Fabrizio, Gogolin, and Nersesyan [Phys. Rev. Lett. 83, 2014 (1999)]: We confirm the existence of the spontaneously dimerized phase as an intermediate state. Further we provide numerical evidence to check the criticalities on the phase boundaries. Especially, we perform the finite-size-scaling analysis of the excitation gap to show the two-dimensional Ising transition in the charge part. On the other hand, we confirm that the dimerized phase survives in the strong-coupling limit, which is one of the resultants of competition between the ionicity and correlation effects.
We investigate the ground state phase diagram of the one-dimensional ionic Hubbard model with an alternating potential at half-filling by the bosonization technique as well as by numerical diagonalization of finite systems with the Lanczos and DMRG methods. Our results support the existence of a single "metallic" transition point from a band to a correlated insulator with simultaneous charge and bond-charge order. In addition, we present results for the optical conductivity obtained by the dynamical DMRG method. The insulator-insulator phase transition scenario is discussed in detail including a critical review of existing approaches and results for the ionic Hubbard model.
Exact ground states, charge densities, and excitation energies are found using valence bond methods for N-site modified Hubbard models with uniform spacing. At the neutral-ionic transition (NIT), the ground state has a symmetry crossover in 4n4n4n and 4n+24n+24n+2 rings with periodic and antiperiodic boundary conditions, respectively. Large site energies $\ensuremath{\Delta}$ stabilize a paired state of the half-filled chain, while large U stabilizes a covalent state. Finite-transfer integrals t shift the NIT to the covalent side of $U\ensuremath{-}2\ensuremath{\Delta}.$ Exact results to N=16N=16N=16 in the full basis and to N=22N=22N=22 in a restricted basis for large U and $\ensuremath{\Delta}$ are extrapolated to obtain the crossover and charge density of extended chains. The modified Hubbard model has a continuous NIT between a diamagnetic band insulator on the paired side and a paramagnetic Mott insulator on the covalent side. The singlet-triplet (ST), singlet-singlet (SS), and charge gaps for finite N indicate that the ST and SS gaps close at the NIT with increasing U, and that the charge gap vanishes only there. Finite-N excitations constrain all singularities to $\ifmmode\pm\else\textpm\fi{}0.1t$ of the symmetry crossover. The NIT is interpreted as a localized ground state (GS) with finite gaps on the paired side and an extended GS with vanishing ST and SS gaps on the covalent side. The charge gap and charge stiffness indicate a metallic GS at the transition that, however, is unconditionally unstable to dimerization. Finite $\ensuremath{\Delta}$ breaks electron-hole $(e\ensuremath{-}h)$ symmetry, but the modified Hubbard model has an extended $e\ensuremath{-}h$ symmetry, and a strong mixing of spin and charge excitations is limited to a few t's about the NIT. Exact finite-size results complement other approaches to valence or ferroelectric transitions in organic charge-transfer salts or in inorganic oxides, and to electron-vibration coupling and structural instabilities in one-dimensional systems.