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arXiv · 2210.09208

Chebyshev pseudosite matrix product state approach for the spectral functions of electron-phonon coupling systems

Pei-Yuan Zhao·Ke Ding·Shuo Yang
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Abstract

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 new and 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, which has not been studied extensively before. 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 (1D) cuprates.

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Pei-Yuan Zhao, Ke Ding, Shuo Yang. 2022-10-17. Chebyshev pseudosite matrix product state approach for the spectral functions of electron-phonon coupling systems. https://doi.org/10.1103/physrevresearch.5.023026

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