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.
We discuss a semiclassical calculation of low energy charge transport in one-dimensional (1D) insulators with a focus on Mott insulators, whose charge degrees of freedom are gapped due to the combination of short range interactions and a periodic lattice potential. Combining RG and instanton methods, we calculate the nonlinear AC conductivity and interpret the result in terms of multi-photon absorption. We compare the result of the semiclassical calculation for interacting systems to a perturbative, fully quantum mechanical calculation of multi-photon absorption in a 1D band insulator and find good agreement when the number of simultaneously absorbed photons is large.
We investigate the two-photon absorption (TPA) spectrum in Mott insulators on the basis of dynamical cluster approximation. The nonlocal correlation is found to be important in enhancing the dimensionality dependence of the TPA spectrum. The dependence of the TPA spectrum on Coulomb interaction is modified compared with that of the dynamical mean field theory, which is also caused by a nonlocal correlation through a one-particle spectrum. We compare several degrees of nonlocality by adjusting the cluster momentum. The iterated perturbation theory is adopted as an impurity solver, and then a comparison with the noncrossing approximation is presented. It is confirmed that the predominant optical process in Mott insulators is different from that of conventional semiconductors, and small Mott insulating gaps are favorable for obtaining a large TPA spectrum.
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.
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.
In this work we investigate charge transport in one-dimensional insulators via semiclassical and perturbative renormalization group methods. We consider the problem of electron-electron, electron-phonon and electron-two-level system interactions. We show that nonlinear collective modes such as polarons and solitons are responsible for transport. We find a new excitation in the Mott insulator: the polaronic soliton. We discuss fhe differences between band and Mott insulators in terms of their spin spectrum and obtain the charge and spin gaps in each one of these systems. We show that electron-electron interactions provide strong renormalizations of the energy scales in the problem.