We present an exact diagonalization study of the single-particle spectral function in the one-dimensional (1D) and two-dimensional (2D)
t-
J model. By studying the scaling properties with
J and
t we find a simple building pattern in 1D and show that every spectral feature can be uniquely assigned by a spinon and holon momentum. We find two types of low-energy excitations: A band with energy scale
J and high spectral weight disperses upwards in the interior part of the Brillouin zone and reaches
EF at
kF, and a band with energy scale
t and low spectral weight disperses downwards in the outer part of the zone, touching
EF at
3kF. An analogous analysis of the 2D case at half-filling shows that the
t band exists also in this case, but is diffuse and never reaches the Fermi energy. For the doped case in 2D the picture is more reminiscent of 1D; in particular, the ``main band'' with a dispersion $\ensuremath{\propto}J$ and the ``shadow band'' with energy scale
t can be identified also in this case. This leads us to propose that the shadow bands discovered by Aebi et al. in Bi2212 are the 2D analog of the
3kF singularity in 1D systems and unrelated to antiferromagnetic spin fluctuations.
We study the spectral function of interacting one-dimensional fermions for an integrable lattice model away from half-filling. The divergent power-law singularity of the spectral function near the single-particle or single-hole energy is described by an effective x-ray edge type model. At low densities and for momentum near the zone boundary, we find a second divergent singularity at higher energies which is associated with a two-particle bound state. We use the Bethe ansatz solution of the model to calculate the exact singularity exponents for any momentum and for arbitrary values of chemical potential and interaction strength in the critical regime. We relate the singularities of the spectral function to the long-time decay of the fermion Green's function and compare our predictions with numerical results from the time-dependent density-matrix renormalization group (tDMRG). Our results show that the tDMRG method is able to provide accurate time decay exponents in the cases of power-law decay of the Green's function. Some implications for the line shape of the dynamical structure factor away from half-filling are also discussed. In addition, we show that 85% of the total spectral weight in the zero field Heisenberg model near wave-vector $q=\ensuremath{\pi}$ is given by the two-spinon contribution.
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.
We exactly calculate the momentum-dependent critical exponents for spectral functions in the one-dimensional anisotropic t-J models with a gap either in the spin or charge excitation spectrum. Our approach is based on the Bethe ansatz technique combined with finite-size scaling techniques in conformal field theory. It is found that the spectral functions show a power-law singularity, which occurs at frequencies determined by the dispersion of a massive spin (or charge) excitation.We discuss how the nontrivial contribution of a massive excitation controls the singular behavior in optical response functions.
Results for the one-particle Green's function for the Tomonaga-Luttinger model of one-dimensional interacting fermions take a simple form using space and time variables. To obtain the corresponding spectral functions which determine photoemission and inverse-photoemission spectra, a double Fourier transform is necessary. For the model including spin we present analytical and numerical results. They show drastic differences from the spinless case. Expressions for the critical indices which determine the singularities of the spectra are given.
We construct the spectral function of the Luther - Emery model which describes one-dimensional fermions with gapless charge and gapped spin degrees of freedom. We find a true singularity with interaction dependent exponents on the gapped spin dispersion and a finite maximum depending on the magnitude of the spin gap on a shifted charge dispersion. We apply these results to photoemission experiments on charge density wave systems and discuss the spectral properties of a one-dimensional Mott insulator.