We examine zero-temperature one-particle spectral functions for the one-dimensional two-band spinless fermions with different velocities and general forward-scattering interactions. By using the bosonization technique and diagonalizing the model to two Tomonaga-Luttinger liquid Hamiltonians, we obtain general expressions for the spectral functions, which are given in terms of the Appell hypergeometric functions. For the case of identical two-band fermions, corresponding to the SU(2) symmetric spin-1/2 fermions with repulsive interactions, the spectral functions can be expressed in terms of the Gauss hypergeometric function and are shown to recover the double-peak structure suggesting the well-known ``spin-charge'' separation. By tuning the difference in velocities for the two-band fermions, we clarify the crossover in spectral functions from the spin-charge separation to the decoupled fermions. We discuss the relevance of our results to the spin-1/2 Hubbard model under a magnetic field, which can be mapped onto two-band spinless fermions.
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.
Although charge-spin separation has important consequences for the properties of one-dimensional (1D) Mott-Hubbard insulators, matrix elements in some of its dynamical correlation functions involve the coupling of spin and charge degrees of freedom. The corresponding interplay of the 1D Mott-Hubbard insulator's charge and spin degrees of freedom is an issue of both fundamental and technological interest, for instance, concerning their dynamics at subpicosecond timescales. On the other hand, the up- and down-spin one-particle spectral functions are the simplest dynamical correlation functions that involve excitation of both the charge and spin degrees of freedom. They are thus suitable to extract basic useful physical information on the above interplay at finite magnetic fields. Here the line shape of such functions at and in the $(k,\ensuremath{\omega})$ plane's vicinity of their cusp singularities is studied for the Mott-Hubbard insulator described by the 1D Hubbard model with one fermion per site at zero and finite magnetic fields. At zero field, they can be accessed in terms of electrons by photoemission experiments. At finite field, such functions and corresponding interplay of correlations and magnetic-field effects refer to an involved nonperturbative many-particle problem that is poorly understood. The Mott-Hubbard gap that separates the addition and removal spectral functions is calculated for all spin densities and interaction values. The qualitative differences in the one-particle properties of the Mott-Hubbard insulator and corresponding doped insulator are also investigated. The relation of our theoretical results and predictions to both condensed-matter and ultracold spin-
1/2 atom systems is discussed.
We consider one-dimensional spin-
21 fermions in a clean quantum wire, with forward scattering interactions and a nonlinear single-particle spectrum ${\ensuremath{\xi}}_{k}=v\ensuremath{\mid}k\ensuremath{\mid}+{k}^{2}∕2m$, where
v is the Fermi velocity and
1∕m is the band curvature. We calculate the dynamical structure factor (DSF) of the model at small wave vector
q with the help of the bosonization technique. For spinless fermions, we show that, starting from the single-parametric spectrum $\ensuremath{\omega}=u\ensuremath{\mid}q\ensuremath{\mid}$, bosonization emulates the two-parametric excitation spectrum $\ensuremath{\omega}=u\ensuremath{\mid}q\ensuremath{\mid}\ifmmode\pm\else\textpm\fi{}{q}^{2}∕2{m}^{*}$, where
m∗ decreases with increasing repulsive interactions. Moreover, away from the excitation cone, i.e., $\ensuremath{\omega}⪢u\ensuremath{\mid}q\ensuremath{\mid}$, bosonization yields the two-pair excitation continuum of the DSF. For spinful fermions, we show that the spin-charge coupling (SCC) due to band curvature affects the charge and spin DSFs in an asymmetric way. For the charge DSF, SCC manifests as a two-peak structure: a charge peak at $\ensuremath{\omega}={u}_{\ensuremath{\rho}}\ensuremath{\mid}q\ensuremath{\mid}$ but also a spin peak at $\ensuremath{\omega}={u}_{\ensuremath{\sigma}}\ensuremath{\mid}q\ensuremath{\mid}$, as charge fluctuations may decay via chargeless spin-singlet excitations. For the magnetic DSF, SCC manifests as a continuous transfer of magnetic spectral weight to frequencies $\ensuremath{\omega}>{u}_{\ensuremath{\sigma}}\ensuremath{\mid}q\ensuremath{\mid}$, as spin fluctuations decay via pairs of chargeless spin and spinless charge-neutral excitations.
The momentum, fermionic density, spin density, and interaction dependencies of the exponents that control the (k,ω)-plane singular features of the one-fermion spectral functions of a one-dimensional gas of spin-1/2 fermions with repulsive delta-function interaction both at zero and finite magnetic field are studied in detail. Our results refer to energy scales beyond the reach of the low-energy Tomonaga-Luttinger liquid and rely on the pseudofermion dynamical theory for integrable models. The one-fermion spectral weight distributions associated with the spectral functions studied in this paper may be observed in systems of spin-1/2 ultra-cold fermionic atoms in optical lattices.
The spectral properties of the spinless fermion model with nearest-neighbor repulsive interactions on a one-dimensional lattice are investigated using the Bethe ansatz. Although its bulk quantities are exactly the same as those of the spin-1/2 XXZ chain, the difference in the statistics of particles causes substantial effects on spectral features, such as gapless points of dispersion relations and line shapes of spectral functions. In this Letter, we clarify the origin of the differences in spectral features between fermionic and bosonic systems in terms of Bethe ansatz solutions. We also confirm that the two-string solutions have considerable spectral weights in the high-energy regime.