Dynamical density matrix renormalization group study of photoexcited states in one-dimensional Mott insulators

Abstract

One-dimensional Mott insulators exhibit giant nonlinear optical response. Based on the dynamical density matrix renormalization group method, photoexcited states and optical response in the insulators are studied as functions of the on-site and the nearest neighbor Coulomb interactions, U and V , respectively. We find that the lowest optically allowed and forbidden excited states across the Mott gap, which have odd and even parities, respectively, are degenerate for V /t < ∼ 2 with t being the hopping integral of an electron between nearest neighbor sites. For V /t > ∼ 2, the bound states with odd and even parities occur and are not degenerate. The nature of the degeneracy and its effect on the optical response are examined.PACS numbers: 71.10. Fd, 72.80.Sk, 78.30.Am In one-dimensional Mott insulators with strong onsite Coulomb interaction U , the ultrafast and gigantic nonlinear optical response have been observed [1,2]. The third-order nonlinear susceptibilities in the typical one-dimensional Mott insulators of charge transfer type, such as cuprates and halogen-bridged Ni-halides, are a thousand times larger than those of band insulators or Peierls insulators [2]. In the previous theoretical investigations [3,4], it has been pointed out that the anomalous enhancement of the nonlinear susceptibilities in the onedimensional Mott insulators originates in the large transition dipole moment between an optically allowed state with odd parity and an optically forbidden (two-photon allowed) state with even parity due to the degeneracy of these states.In the large-U limit, only the charge degree of freedom survives in the photoexcited states due to the spincharge separation [5], and the system is well described by an effective two particle model, called the holon-doublon model, which is composed of a holon representing one photoinduced empty site and a doublon representing one doubly occupied site with the attractive Coulomb interaction −V between them. When V exceeds a critical value V = 2t, these paricles form an excitonic bound state [6]. Since these two particles cannot exchange each other, the photoexcited states with odd and even parities are degenerate regardless of the magnitude of V . By using this model, the experimentally obtained optical spectra for the cuprates have been analyzed. However, the optical gap in the compounds is finite (∼ 2 eV) and thus the holon-doublon model, which is obtained in the limit of large U , may be re-examined. Under a finite-U condition, there is an intermediate process that these particles recombine, while this process is prohibited in the large-U limit. Since, in the finite-U condition, these particle can exchange their positions through the intermediate process, the eigenenergies of the odd-and even-parity states * Electronic address: matsueda@imr.tohoku.ac.jp may be different. Therefore, it is indispensable to clarify the optical response in Mott insulators with finite U .The minimal model to describe photoexcitation in the Mott insulators is the single-band extended Hubba...

Excitonic effect on the optical response in the one-dimensional two-band Hubbard model

“…The free carrier motion is supported from an analytical method. 6 It is also noted that a small hump structure seen around =2=⌬ in Fig. 1͑h͒ is due to the boundary effect.…”

“…A numerical simulation technique applied here is the DDMRG method. [6][7][8][9][10][11][15][16][17] With changing ⌬ / t and V / t systematically, we find that the low-energy peak of the correlation function consists of a single Lorentzian component for a parameter range appropriate to the compounds. This is due to the excitonic state induced by V, and consistent with the optical absorption spectra of the compounds.…”

“…The photoexcited states and optical response of the model have been examined by employing the dynamical density matrix renormalization group ͑DDMRG͒ method. [6][7][8][9][10][11] The model and the method are suitable for the clarification of the general electronic properties of the insulators. However, the real compounds such as the cuprates and the halogen-bridged Ni-compounds are the insulators of charge transfer type, where both half-filled d-orbitals and empty p-orbitals for holes exist in onedimensional networks of the transition metal and ligand ions.…”

Photoinduced Charge and Spin Dynamics in Strongly Correlated Electron Systems

“…Theoretical treatment of manybody interactions, dynamical response, and time dependence due to nonequilibrium states on an equal footing is challenging [11,12]. In order to overcome this difficulty, we perform a density matrix renormalization group (DMRG) calculation [13,14,15,16,17,18,19]. We find that the spectral weight above the COI gap is transferred into lower-energy region just after the photoirradiation, and then tends to go back to higher-energy region.…”

“…Here, we take L = 13 and the electron number N el = 7. The density matrix of the system block is defined by [14,15,16,17,18,19]. The truncation number is m = 256.…”