The joint valence band photoemission spectrum and BIS of an N fold degenerate Hubbard model is calculated using a 1/N expansion, that retains the coherence of the lattice. The lowest order term in the expansion constitutes a Hartree-Fock mean field theory, and to next leading order one finds that the dynamics are dominated by boson like collective excitations. The one electron spectra are, generally, found to have long tails, however in the vicinity of the Fermi-level the spectra shows narrow features. The appearance of satellites and large mass enhancements are correlated with the softening of the boson modes.
We calculate the photoemission/inverse photoemission spectrum for an N-fold degenerate Hubbard model, in the 1/N approximation. The spectra are broadened, and for sufficiently large Coulomb interaction strengths the spectra show satellites both in the photoemission and the brehmstrahlung isochromat spectroscopy portions of the spectra. The intensity of the spectra at the fermi level are equal to the noninteracting values, in accordance with Luttinger’s theorem. We show that this can result in a temperature-dependent peak at the Fermi level; the width of the peak is governed by the quasi-particle lifetime. We relate the temperature dependent peak to the Fermi-liquid properties.
We analyze the single-particle and collective excitations near the metal to charge-transfer insulator transition, using the slave-boson technique. We show that the Mott transition can be interpreted as a softening of an auxiliary Bose excitation. In the insulating phase the energy of the boson at zero momentum is related to the jump in the chemical potential at zero doping. The dispersion of the collective modes gives rise to the structure of the incoherent Hubbard bands. A similar picture holds for the single-band Hubbard model.
We study the relation between the microscopic properties of a many-body system and the electron spectra, experimentally accessible by photoemission. In a recent paper [O. Gunnarsson et al., Phys. Rev. Lett. 114, 236402 (2015)], we introduced the ``fluctuation diagnostics'' approach to extract the dominant wave-vector-dependent bosonic fluctuations from the electronic self-energy. Here, we first reformulate the theory in terms of fermionic modes to render its connection with resonance valence bond (RVB) fluctuations more transparent. Second, by using a large-
U expansion, where
U is the Coulomb interaction, we relate the fluctuations to real-space correlations. Therefore, it becomes possible to study how electron spectra are related to charge, spin, superconductivity, and RVB-like real-space correlations, broadening the analysis of an earlier work [J. Merino and O. Gunnarsson, Phys. Rev. B 89, 245130 (2014)]. This formalism is applied to the pseudogap physics of the two-dimensional Hubbard model, studied in the dynamical cluster approximation. We perform calculations for embedded clusters with up to 32 sites, having three inequivalent
K points at the Fermi surface. We find that as
U is increased, correlation functions gradually attain values consistent with an RVB state. This first happens for correlation functions involving the antinodal point and gradually spreads to the nodal point along the Fermi surface. Simultaneously, a pseudogap opens up along the Fermi surface. We relate this to a crossover from a Kondo-type state to an RVB-like localized cluster state and to the presence of RVB and spin fluctuations. These changes are caused by a strong momentum dependence in the cluster bath couplings along the Fermi surface. We also show, from a more algorithmic perspective, how the time-consuming calculations in fluctuation diagnostics can be drastically simplified.
As a generic model describing quasi-one-dimensional Mott and Peierls insulators, we investigate the Holstein-Hubbard model for half-filled bands using numerical techniques. Combining Lanczos diagonalization with Chebyshev moment expansion we calculate exactly the photoemission and inverse photoemission spectra, and use these to establish the phase diagram of the model. While polaronic features emerge only at strong electron-phonon couplings, pronounced phonon signatures, such as multiquanta band states, can be found in the Mott insulating regime as well. In order to corroborate the Mott to Peierls transition scenario, we determine the spin- and charge-excitation gaps by a finite-size scaling analysis based on density-matrix renormalization-group calculations.
We theoretically study photoemission spectra for photodoped one-dimensional Mott insulators that can host excitons, and show that their spectral characteristics differ qualitatively from those of photodoped semiconductors. In conventional semiconductors, photoemission spectra are well understood; free charge carriers generate spectral weight near the bottom of the conduction band, while the formation of excitons leads to replica features of the valence band appearing inside the band gap. In one-dimensional Mott insulators, on the other hand, strong correlations give rise to fractionalized elementary excitations-spinons, holons, and doublons-which fundamentally modify the photoemission response. We find that when photodoped carriers, i.e., doublons and holons, remain unbound, the photoemission spectrum directly reflects the dispersion of spinons, i.e., magnetic elementary excitations. In contrast, when a doublon and a holon form an excitonic bound state, replica structures of the lower Hubbard band emerge inside the Mott gap, carrying contributions from both spinon and holon excitations. Importantly, the distribution of the in-gap signal depends sensitively on the degree of doublon-holon binding. The origin of these spectral features is clarified through a combination of exact diagonalization and the slave-particle approach. These results indicate that photoemission from photoinduced carriers and excitons in strongly correlated electron systems can provide information on magnetic properties and carrier-binding properties.
Using the Hubbard model and the corresponding t-J model, we study the properties of correlated states with valence-bond structures. Mixed states with such structures and with antiferromagnetic spin ordering can be constructed by means of local unitary transformations of uncorrelated states. The latter turn out to have lower energy than mean-field antiferromagnetic solutions. Spin correlations for various degrees of doping δ = n −1 are in good agreement with the results of exact calculations for finite systems. In contrast to mean-field solutions, allowance for valence-bond correlations leads to a reasonable value of the critical δ , at which long-range antiferromagnetic order disappears. A calculation of the spectral functions that describe photoemission reveals typical behavior in two bands of effective hole (and electron) excitations, and energy transport in bands as the quasimomentum varies from (0,0) to ( π,π ), consistent with calculations in finite systems. We construct a homogeneous correlated state of fluctuating valence bonds (the band-model analog of states of fluctuating valence bonds), and demonstrate that its energy is lower than that of valence-bond alternant structures.