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

TL;DR

This paper introduces a novel Chebyshev pseudosite MPS method combined with pseudosite DMRG to efficiently compute spectral functions in complex electron-phonon systems, enabling new insights into strongly correlated models.

Contribution

The paper develops a new computational approach that maps bosonic phonon degrees of freedom onto pseudosites within the MPS framework, allowing efficient spectral function calculations for complex e-ph systems.

Findings

Weak extended e-ph couplings enhance spectral weight of holon-folding branch.

Method captures key spectral features at modest computational cost.

Results align with photoemission observations in 1D cuprates.

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.