We present an efficient numerical method for the description of ground state and spectral properties of a doped hole in generalized $t\text{\ensuremath{-}}J$ models coupled to optical phonons. In the weak-coupling regime, coherent hole motion is less affected by the electron-phonon (EP) interaction in the electron than in the hole-doped system. Increasing the strength of EP coupling leads to a vanishing low-energy spectral weight around $\ensuremath{\Gamma}$ point. Spectral properties are in the strong coupling regime consistent with recent high-resolution angle resolved photoemission spectra (ARPES) [K. M. Shen et al., Phys. Rev. Lett. 93, 267002 (2004)]. A waterfall-like feature appears connecting the dispersive low-energy band with the incoherent high-energy peak resembling ARPES data [F. Ronning et al., Phys. Rev. B 71, 094518 (2005)].
We use density matrix renormalization group (DMRG) and variational exact diagonalization (VED) to calculate the single-electron removal spectral weight for the Hubbard-Holstein model at low electron densities. Tuning the strength of the electron-phonon coupling and of the Hubbard repulsion allows us to contrast the results for a liquid of polarons versus a liquid of bipolarons. The former shows spectral weight up to the Fermi energy, as expected for a metal. The latter has a gap in its spectral weight, set by the bipolaron binding energy, although this is also a (strongly correlated) metal. This difference suggests that angle-resolved photoemission spectroscopy could be used to identify liquids of pre-formed pairs. Furthermore, we show that the one-dimensional liquid of incoherent bipolarons is well approximated by a "Bose sea" of bosons that are hard-core in momentum space, occupying the momenta inside the Fermi sea but otherwise noninteracting. This new proposal for a strongly correlated many-body wave function opens the way for studying various other properties of incoherent (nonsuperconducting) liquids of preformed pairs in any dimension.
In this paper we study the scattering theory associated with the pseudofermion dynamical theory for the Hubbard chain. In terms of pseudofermions the spectral properties are controlled by zero-momentum forward scattering only. The pseudofermion
S matrix is expressed as a commutative product of
S matrices, each corresponding to an elementary two-pseudofermion scattering event. This commutative factorization is stronger than the usual factorization associated with Yang-Baxter Equation for the original spin 1/2 electron bare
S matrix. Our results reveal the scattering mechanisms which control the exotic finite-energy spectral properties of the low-dimensional complex materials and correlated systems of cold fermionic atoms on an optical lattice. Importantly, the exotic scatterers and scattering centers predicted by the theory were observed by angle-resolved photoelectron spectroscopy in low-dimensional organic metals.