| Summary: | The electron-phonon (e-ph) coupling system often has a large number of phonon degrees of freedom, whose spectral functions are numerically difficult to compute using matrix product state (MPS) formalisms. To solve this problem, we propose a practical method that combines the Chebyshev MPS and the pseudosite density matrix renormalization group (DMRG) algorithm. The Chebyshev vector is represented by a pseudosite MPS with global U(1) fermion symmetry, which maps 2^{N_{p}} bosonic degrees of freedom onto N_{p} pseudosites, each with two states. This approach can handle arbitrary e-ph coupling Hamiltonians where pseudosite DMRG performs efficiently. We use this method to study the spectral functions of the doped extended Hubbard-Holstein model in a regime of strong Coulomb repulsion. Key features of the excitation spectra are captured at a modest computational cost. Our results show that weak extended e-ph couplings can increase the spectral weight of the holon-folding branch at low phonon frequencies, in agreement with angle-resolved photoemission observations on one-dimensional cuprates.
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