We develop a path-integral formulation which is free from Grassmann algebras to calculate absorption spectra of strongly correlated electron systems. The Coulomb repulsions, including not only the short-range part but also a long-range part, are reduced into a time-dependent one-body Hamiltonian with only two kinds of Ising spin variables per site. The sums over these spin configurations are performed according to the quantum Monte Carlo techniques. By this method we disclose the electron correlation effects on absorption spectra. The method is applied to the one-dimensional half-filled electron systems, where the ground state is an insulating state due to the strong long-range Coulomb repulsion and contains large quantum fluctuations by low-energy collective spin excitations. The absorption spectrum shows an infrared divergencelike structure, which seems to arise from the simultaneous excitation of the charge-transfer exciton and collective spin excitations. The spectrum also contains new peaks on the high energy side which correspond to the multiple excitation of electron-hole pairs. Such a multiple excitation is caused by the electron correlation effect, through which the photogenerated electron and hole can excite other electron-hole pairs. Our result clearly shows that charge and spin of the electron are inseparable in a many-body system in an insulating state caused by the strong long-range Coulomb repulsion.
Electron correlation effects on the Lehmann spectra of the one-body Green functions are clarified by using the quantum Monte Carlo simulation of path-integral form. Through the analysis of the Lehmann spectrum, we also show that the electron states of the insulating systems caused by the Coulomb repulsion (Mott-type insulators) significantly depend on the strength of the Coulomb interaction. Specifically, it is shown that in the weak interaction regime, the momentum-specified Lehmann spectrum is qualitatively explained by the second order perturbation theory from the unrestricted Hartree-Fock state, especially near the Fermi energy. This means that the Lehmann spectrum still has a dominant one-body component. On the other hand, in the strong interaction regime, the Lehmann spectrum loses such a one-body component almost completely even near the Fermi energy, and is constituted of the many-body component caused by the coupling between the charge and magnetic excitations. These results indicate that in the weak interaction regime, the electron state of the Mott-type insulator can be described by the one-body picture near the Fermi energy, while in the strong interaction regime, such a one-body picture no longer works even near the Fermi energy. For these two cases, the Lehmann spectra have clearly different peak structures. Since the Lehmann spectrum corresponds to the photoemission spectrum in experiment, we conclude that photoemission spectroscopy can be a valuable tool to obtain direct information on the strength of the Coulomb interaction.
We show that charge excitations within one-dimensional extended Hubbard models in the limit of large on-site Coulomb interaction can be mapped onto pairs of spin reversals from the ferromagnetic Ising-Heisenberg spin Hamiltonian. The exciton in the extended Hubbard models is equivalent to the bound two-magnon state of the spin Hamiltonian. From exact results for the spin Hamiltonian, for the intersite Coulomb interactions limited between nearest neighbors, the lowest optical exciton is separated in energy from the electron-hole continuum only for the intersite interaction larger than half the one-electron bandwidth. The commutation relationship between spin operators allows us to numerically investigate exciton binding energies and optical absorptions from the ground state in the limit of large on-site Coulomb interaction even for cases where analytic results are not available. For intersite Coulomb interaction limited between nearest neighbors, the binding energy of the lowest optical exciton changes very weakly for realistic Peierls bond dimerization, although there is a profound change in the optical absorption. While in the undimerized chain a single optical exciton can occur, two additional excitons that occur above the threshold of the electron-hole continuum become optically visible in the dimerized case. For long-range intersite Coulomb interactions, multiple excitons can occur even for the undimerized chain, and additional exciton states become optically visible upon dimerization. With the
1/r form for the intersite Coulomb interaction, our numerical calculations suggest that the formation of at least one optical exciton is unconditional, unlike the case of nearest-neighbor interaction. The binding energy of the lowest optical exciton again depends weakly on the dimerization for long-range interaction. Our theoretical results can explain the occurrence of two charge-transfer absorption bands in half-filled band segregated stack charge transfer solids below the spin-Peierls dimerization temperature. Our results also suggest that the lowest optical state of \ensuremath{\pi}-conjugated polymers, in which Coulomb interactions are long ranged, is necessarily an exciton.
We formulate a new theory for optical response of many-electron systems in insulating states coming from strong electron-phonon (e-ph) and electron-electron (e-e) interactions. The e-ph coupling and the short range part of e-e repulsion are reduced into a time-dependent one-body Hamiltonian by the path-integral. While, the long range part of e-e repulsion is taken into account straightly, as a perturbation to this time-dependent Hamiltonian. To evaluate higher order terms of this perturbation, we have extended the Bloch-De Dominicis theorem, so that it can be used even in the cases where an unperturbud one-body Hamiltonian is time-dependent, as well as in the conventional time-independent cases. Using this theorem, we have formulated the optical response, wherein the long range part results in exciton effects or particle-hole attractions as a final-state interaction of the optical transition. Another path-integral is also formulated, in which the short and long range parts are treated on an equal footing.
We theoretically investigate the light absorption spectrum of two-dimensional (2D) Mott insulators. We employ the numerical diagonalization method to calculate the light absorption spectrum with using the effective Hamiltonian for the extended Hubbard model, which is valid when the on-site Coulomb interaction energy
U is much larger than the nearest-neighbor transfer integral
t and the nearest-neighbor Coulomb interaction energy
V. For
V=0, the absorption spectrum consists of a broad band with a width of about
16t and a sharp central peak, and the energy eigenstates contributing to the absorption spectrum do not have the antiferromagnetic (AF) spin order, when
U is sufficiently larger than
t. These features result from the spin-charge interplay inherent in the very strong correlation region where charge transfer term is dominant. With decreasing
U∕t, the peak structure in absorption spectrum becomes unclear and some low energy eigenstates have the AF spin order, as a result of the spin-spin interaction term. For large
V∕t, the dominant peak arises in the lower energy region of the spectrum. A large number of holon-doublon bound states, which have nearly the same charge but different spin structures, are responsible for this peak, in contrast to the conventional exciton state. This is also in contrast to the charge bound states in one-dimensional (1D) Mott insulators, where a single energy eigenstate dominates the optical transition moment as a result of the spin-charge separation. The essentially different absorption spectra between the 1D and 2D Mott insulators originate from the difference in the coupling between spin and charge degrees of freedom.
The effective Hamiltonian of the Hubbard model for multiphoton excited states is derived assuming a strong Coulomb repulsion. Diagonalizing the effective Hamiltonian exactly, the lowest energy one-photon excited state is calculated in the two-dimensional Hubbard model at half-filling, and its physical properties are investigated. For
t/U< 0.0165, where t is the magnitude of the transfer integral between the nearest-neighbor sites and U is an on-site Coulomb repulsion energy, ferromagnetic spin order is photogenerated from the antiferromagnetic ground state, and, for
t/U> 0.0166, antiferromagnetic spin order survives one-photon excitation. Photoinjected opposite charges are unbound because of strong electron correlation for
t/U< 0.08, and bound for
t/U> 0.08. The probability that the photoinjected opposite charges are on nearest-neighbor sites is strongly suppressed through all the correlation regions including this charge-bound region. We see a tendency toward spin-charge separation, but the coupling is not small in the one-photon excited state. The local spin structure around the bound positive and negative charges injected by photoexcitation is quite different from that induced by two-hole doping; this result suggests that multiphoton excitation will generate an electronic order which differs from that generated by doping.
We study the optical properties of an electron–hole two-band Hubbard model with interactions of electron–electron (hole–hole) repulsion U and electron–hole attraction U '. In the case of two types of correlated insulators at half filling, viz. , the Mott–Hubbard type and the biexciton type, interband linear absorption/gain spectra including excitonic effects are calculated analytically using two-site dynamical mean-field theory and ladder approximation. We show that an exciton-like peak structure emerges because of an “exciton” in the sea of correlated fermions when U ' is larger than a certain critical value. The binding energy of the photoinduced excitonic bound state and the spectral intensity are evaluated as a function of U '. The emergence and absence of the exciton-like peak suggests that there are two different insulating mechanisms in the Mott–Hubbard insulating state of the electron–hole system: one is attributable to only U and the other is attributable to both U and U '; the latter is called the excitonic Mott–Hubbard insulating state. The intrinsic difference of the mechanisms cannot be captured from only single-particle properties such as the density of states, but it appears clearly in optical properties reflecting two-particle correlations.