The variational cluster approximation is used to study the spontaneous symmetry breaking of the excitonic insulator (EI) state in the two-orbital Hubbard model defined on the two-dimensional square lattice. Evaluating the order parameter of the EI state, staggered magnetization, and number of particles on each orbital, we obtain the ground-state phase diagram of the model in a wide parameter space of the intra and interorbital Coulomb interactions. We also calculate the single-particle and anomalous Green's functions. We show that the normal metallic phase is unstable to the formation of the EI state and the EI phase appears in a wide parameter region between the band-insulator and Mott-insulator phases.
Using the variational cluster approach based on the self-energy functional theory, we study the possible occurrence of excitonic order and superconductivity in the two-orbital Hubbard model with intra- and inter-orbital Coulomb interactions. It is known that an antiferromagnetic Mott insulator state appears in the regime of strong intra-orbital interaction, a band insulator state appears in the regime of strong inter-orbital interaction, and an excitonic insulator state appears between them. In addition to these states, we find that the
s±-wave superconducting state appears in the small-correlation regime, and the
dx2−y2-wave superconducting state appears on the boundary of the antiferromagnetic Mott insulator state. We calculate the single-particle spectral function of the model and compare the band gap formation due to the superconducting and excitonic orders.
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 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 real part of optical conductivity $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ of the Mott insulators has a large amount of information on how spin and charge degrees of freedom interact with each other. By using the time-dependent density-matrix renormalization group, we study $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ of the two-dimensional Hubbard model on a square lattice at half filling. We find an excitonic peak at the Mott-gap edge of $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ not only for the two-dimensional square lattice but also for two- and four-leg ladders. For the square lattice, however, we do not clearly find a gap between an excitonic peak and continuum band, which indicates that a bound state is not well defined. The emergence of an excitonic peak in $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ implies the formation of a spin polaron. Examining the dependence of $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ on the on-site Coulomb interaction and next-nearest-neighbor hoppings, we confirm that an excitonic peak is generated from a magnetic effect. Electron scattering due to an electron-phonon interaction is expected to easily suppress an excitonic peak since spectral width of an excitonic peak is very narrow. Introducing a large broadening in $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ by modeling the electron-phonon coupling present in
La2CuO4 and
Nd2CuO4, we obtain $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ comparable with experiments.
The electronic properties of excitonic insulators have been examined precisely in recent years. Pictures of exciton condensation may be applied to the spin-state transition observed in perovskite cobalt oxides. We examine the crystal-field and magnetic-field dependences of spatial spin structures on the basis of the density matrix renormalization group method using an effective model for the one-dimensional two-orbital Hubbard model in strong-coupling limit. We find an excitonic insulating (EI) phase and a spin-state ordering (SSO) phase in the intermediate region between low-spin and high-spin phases. In the EI phase, spin-triplet excitons are spatially fluctuating due to quantum effects, and an incommensurate spin correlation realizes. The analyses of a spin gap and degeneracy of entanglement spectra suggest the realization of the Haldane-like edge state in the EI phase. In the SSO phase, 3-fold or incommensurate SSO structures realize depending on the crystal-field splitting. These structures are stabilized as a result of the competition of exchange interactions between spin states.