New approach to extract important degrees of freedom in quantum dynamics using singular value decomposition: Application to linear optical spectrum in two-dimensional Mott insulators

We propose a new approach to extract the important degrees of freedom in quantum dynamics induced by an external stimulus. We calculate the coefficient matrix numerically, where the $i-l$ element of the matrix is the coefficient of the lth basis state at the ith discretized time in the solution of the time-dependent Schr\"odinger equation induced by the external stimulus. By performing a randomized singular value decomposition of the coefficient matrix, a practically exact solution is obtained using a linear combination of the important modes, where the number of modes is much smaller than the dimensions of the Hilbert space in many cases. We apply this method to analysis of the light absorption spectrum in two-dimensional (2D) Mott insulators using an effective model of the 2D Hubbard model in the strong interaction case. From the dynamics induced by an ultrashort weak light pulse, we find that the practically exact light absorption spectrum can be reproduced by as few as 1000 energy eigenstates in the $1.7 \times 10^{7}$-dimension Hilbert space of a 26-site cluster. These one-photon active energy eigenstates are classified into free holon and doublon (H-D) and localized H-D states. In the free H-D states, the main effect of the spin degrees of freedom on the transfer of a holon (H) and a doublon (D) is the phase shift, and the H and the D move freely. In the localized H-D states, an H and a D are localized with relative distances of $\sqrt{5}$ or $\sqrt{13}$. The antiferromagnetic (AF) spin orders in the localized H-D states are much stronger than those in the free H-D states, and the charge localization is of magnetic origin. There are sharp peaks caused by excitations to the localized H-D states below the broad band caused by excitations to the free H-D states in the light absorption spectrum

Charge-Transfer Excitations in One-Dimensional Dimerized Mott Insulators

We investigate the optical properties of one-dimensional (1D) dimerized Mott insulators using the 1D dimerized extended Hubbard model. Numerical calculations and a perturbative analysis from the decoupled-dimer limit clarify that there are three relevant classes of charge-transfer (CT) states generated by photoexcitation: interdimer CT unbound states, interdimer CT exciton states, and intradimer CT exciton states. This classification is applied to understanding the optical properties of an organic molecular material, 1,3,5-trithia-2,4,6-triazapentalenyl (TTTA), which is known for its photoinduced transition from the dimerized spin-singlet phase to the regular paramagnetic phase. We conclude that the lowest photoexcited state of TTTA is the interdimer CT exciton state and the second lowest state is the intradimer CT exciton state.Comment: 6 pages, 6 figures, to be published in J. Phys. Soc. Jp

Angle-resolved photoemission study of MX-chain compound [Ni(chxn)2_2Br]Br2_2

We report on the results of angle-resolved photoemission experiments on a quasi-one-dimensional $MX$-chain compound [Ni(chxn)$_2$Br]Br$_2$ (chxn = 1$R$,2$R$-cyclohexanediamine), a one-dimensional Heisenberg system with $S=1/2$ and $J \sim 3600$ K, which shows a gigantic non-linear optical effect. A "band" having about 500 meV energy dispersion is found in the first half of the Brillouin zone $(0\le kb/\pi <1/2)$, but disappears at $kb / \pi \sim 1/2$. Two dispersive features, expected from the spin-charge separation, as have been observed in other quasi-one-dimensional systems like Sr$_2$CuO$_3$, are not detected. These characteristic features are well reproduced by the $d$-$p$ chain model calculations with a small charge-transfer energy $\Delta$ compared with that of one-dimensional Cu-O based compounds. We propose that this smaller $\Delta$ is the origin of the absence of clear spin- and charge-separation in the photoemission spectra and strong non-linear optical effect in [Ni(chxn)$_2$Br]Br$_2$.Comment: 4 pages, 3 figure

Photoinduced Structural Phase Transitions in Polyacene

There exist two types of structural instability in polyacene: double bonds in a cis pattern and those in a trans pattern. They are isoenergetic but spectroscopically distinct. We demonstrate optical characterization and manipulation of Peierls-distorted polyacene employing both correlated and uncorrelated Hamiltonians. We clarify the phase boundaries of the cis- and trans-distorted isomers, elucidate their optical-conductivity spectra, and then explore their photoresponses. There occurs a photoinduced transformation in the polyacene structure, but it is one-way switching: The trans configuration is well convertible into the cis one, whereas the reverse conversion is much less feasible. Even the weakest light irradiation can cause a transition of uncorrelated electrons, while correlated electrons have a transition threshold against light irradiation.Comment: 14 pages with 15 figures embedde

Effects of Lattice and Molecular Phonons on Photoinduced Neutral-to-Ionic Transition Dynamics in Tetrathiafulvalene-pp-Chloranil

For electronic states and photoinduced charge dynamics near the neutral-ionic transition in the mixed-stack charge-transfer complex tetrathiafulvalene-$p$-chloranil (TTF-CA), we review the effects of Peierls coupling to lattice phonons modulating transfer integrals and Holstein couplings to molecular vibrations modulating site energies. The former stabilizes the ionic phase and reduces discontinuities in the phase transition, while the latter stabilizes the neutral phase and enhances the discontinuities. To reproduce the experimentally observed ionicity, optical conductivity and photoinduced charge dynamics, both couplings are quantitatively important. In particular, strong Holstein couplings to form the highly-stabilized neutral phase are necessary for the ionic phase to be a Mott insulator with large ionicity. A comparison with the observed photoinduced charge dynamics indicates the presence of strings of lattice dimerization in the neutral phase above the transition temperature.Comment: 9 pages, 7 figures, accepted for publication in J. Phys. Soc. Jp

Topological (Sliced) Doping of a 3D Peierls System: Predicted Structure of Doped BaBiO3

At hole concentrations below x=0.4, Ba_(1-x)K_xBiO_3 is non-metallic. At x=0, pure BaBiO3 is a Peierls insulator. Very dilute holes create bipolaronic point defects in the Peierls order parameter. Here we find that the Rice-Sneddon version of Peierls theory predicts that more concentrated holes should form stacking faults (two-dimensional topological defects, called slices) in the Peierls order parameter. However, the long-range Coulomb interaction, left out of the Rice-Sneddon model, destabilizes slices in favor of point bipolarons at low concentrations, leaving a window near 30% doping where the sliced state is marginally stable.Comment: 6 pages with 5 embedded postscript figure

Density of Neutral Solitons in Weakly Disordered Peierls Chains

We study the effects of weak off-diagonal disorder on Peierls systems with a doubly degenerate ground state. We show that for these systems disorder in the electron hopping amplitudes induces a finite density of solitons in the minimal-energy lattice configuration of a single chain. These disorder-induced dimerization kinks are neutral and have spin 1/2. Using a continuum model for the Peierls chain and treating the lattice classically, we analytically calculate the average free energy and density of kinks. We compare these results to numerical calculations for a discrete model and discuss the implications of the kinks for the optical and magnetic properties of the conjugated polymer trans-polyacetylene.Comment: 28 pages, revtex, 5 Postscript figures, to appear in Phys. Rev.