We study the effect of varying the boundary condition on: the spectral function of a finite one-dimensional Hubbard chain, which we compute using direct (Lanczos) diagonalization of the Hamiltonian. By direct comparison with the two-body response functions and with the exact solution of the Bethe ansatz equations, we can identify both spinon and holon features in the spectra. At half-filling the spectra have the well-known structure of a low-energy holon band and its shadow-which spans the whole Brillouin zone-and a spinon band present for momenta less than the Fermi momentum. Features related to the twisted boundary condition are cusps in the spinon band. We show that the spectral building principle, adapted to account for both the finite system size and the twisted boundary condition, describes the spectra well in terms of single spinon and holon excitations. We argue that these finite-size effects are a signature of spin-charge separation and that their study should help establish the existence and nature of spin-charge separation in finite-size systems.
We study the effect of varying the boundary condition on the spectral function of a finite one-dimensional Hubbard chain, which we compute using direct (Lanczos) diagonalization of the Hamiltonian. By direct comparison with the two-body response functions and with the exact solution of the Bethe ansatz equations, we can identify both spinon and holon features in the spectra. At half-filling the spectra have the well-known structure of a low-energy holon band and its shadow---which spans the whole Brillouin zone---and a spinon band present for momenta less than the Fermi momentum. Features related to the twisted boundary condition are cusps in the spinon band. We show that the spectral building principle, adapted to account for both the finite system size and the twisted boundary condition, describes the spectra well in terms of single spinon and holon excitations. We argue that these finite-size effects are a signature of spin-charge separation and that their study should help establish the existence and nature of spin-charge separation in finite-size systems.
The effect of a spin gap on the photoemission spectral functions is studied in the one-dimensional t - J X X Z model. We find that spinon bands show up in the spectral functions but holon bands are obscured in the spin-gap cases. The reason for this is studied using a simple interpretation of the spectral functions, which is a convolution between the spectral function of spinless fermions and a spin excitation weight Z ( Q ). The spin gap suppresses the singularity of Z ( Q ), and as a result, only the holon bands are obscured. It is also shown that the spinon peaks lie along a cosine band and extend over the region | k |> k F . Finally, the momentum-dependent critical exponents of the power-law singularity at the spinon bands are determined.
We calculate the spectral function of the one-dimensional Hubbard-Holstein model using the time-dependent density matrix renormalization group, focusing on the regime of large local Coulomb repulsion, and away from electronic half-filling. We argue that, from weak to intermediate electron-phonon coupling, phonons interact only with the electronic charge, and not with the spin degrees of freedom. For strong electron-phonon interaction, spinon and holon bands are not discernible anymore and the system is well described by a spinless polaronic liquid. In this regime, we observe multiple peaks in the spectrum with an energy separation corresponding to the energy of the lattice vibrations (i.e., phonons). We support the numerical results by introducing a well controlled analytical approach based on Ogata-Shiba's factorized wave function, showing that the spectrum can be understood as a convolution of three contributions, originating from charge, spin, and lattice sectors. We recognize and interpret these signatures in the spectral properties and discuss the experimental implications.
Recent advances in numerical analytic continuation with physics-motivated constraints allow sharp spectral features to be extracted from imaginary-time quantum Monte Carlo (QMC) data. We apply these methods to one-dimensional
S=1/2 spin systems with a single ejected fermion, computing the momentum- and energy-dependent single-hole spectral function
A(k,ω). The real-space Green's function
G(r,τ) is evaluated using Angelucci's canonical transformation [Phys. Rev. B 51, 11580 (1995)] implemented within stochastic series expansion QMC, and
A(k,ω) is obtained by constrained stochastic analytic continuation. We contrast systems exhibiting spin-charge separation with those forming a spin polaron through effective spin-charge attraction. For the conventional
t-
J chain, we recover the established signatures of spin-charge separation. Adding a multispin interaction
Q drives the system into a spontaneously dimerized valence-bond-solid (VBS) state; spin-charge-separation features persist up to the transition. Although the spectra generally agree with the conventional analytical ansatz, we find a gap between two holon bands that the ansatz predicts to be degenerate at
k=0 and
k=π. Deep in the VBS phase, the spectra provide evidence for spinon-holon binding at large
Q/J. In a statically dimerized
t-
J chain, we observe equally spaced spin-polaron bands associated with increasingly large bound states and two internal modes, even and odd under parton permutation. These results demonstrate the power of constrained analytic continuation combined with large-scale QMC for resolving sharp spectral features and distinguishing fractionalized from bound excitations.