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

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.

12 pages, 8 figures, new results added

References in corpus (34)

• Array Programming with NumPy
• The density-matrix renormalization group in the age of matrix product states
• Real time evolution using the density matrix renormalization group
• The Kernel Polynomial Method
• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Matrix product states represent ground states faithfully
• DMRG and periodic boundary conditions: a quantum information perspective
• From density-matrix renormalization group to matrix product states
• Tensor network states and algorithms in the presence of a global U(1) symmetry
• Efficient DMFT-simulation of the Holstein-Hubbard Model
• Generic Construction of Efficient Matrix Product Operators
• Anomalously Strong Near-Neighbor Attraction in Doped 1D Cuprate Chains
• Chebyshev matrix product state approach for spectral functions
• The Green's Function of the Holstein Polaron
• Phonon-Mediated Long-Range Attractive Interaction in One-Dimensional Cuprates
• Tensor operators: constructions and applications for long-range interaction systems
• Metallicity in the half-filled Holstein-Hubbard model
• Phase diagram for the one-dimensional Hubbard-Holstein model: A density-matrix renormalization group study
• Phase diagram of the one dimensional Hubbard-Holstein Model at 1/2 and 1/4 filling
• Spectral functions and time evolution from the Chebyshev recursion
• Quantum lattice dynamical effects on the single-particle excitations in 1D Mott and Peierls insulators
• Field-induced polaron formation in the Holstein-Hubbard model
• Strong Coupling Limit of the Holstein-Hubbard Model
• Excitation spectra and spin gap of the half-filled Holstein-Hubbard model
• Finite-temperature density-matrix renormalization group method for electron-phonon systems: Thermodynamics and Holstein-polaron spectral functions
• Pair-Density-Wave in the Strong Coupling Limit of the Holstein-Hubbard model
• Quantum dynamics simulation of intramolecular singlet fission in covalently linked tetracene dimer
• Effect of Electron-Phonon Interaction Range for a Half-Filled Band in One Dimension
• Efficient and Flexible Approach to Simulate Low-Dimensional Quantum Lattice Models with Large Local Hilbert Spaces
• Comparative Study of State-of-the-Art Matrix-Product-State Methods for Lattice Models with Large Local Hilbert Spaces
• Phonon spectral function of the one-dimensional Holstein-Hubbard model
• Emergence of states in the phonon spectral function of the Holstein polaron below and above the one-phonon continuum
• Phonon spectral function of the Holstein polaron
• Interplay of charge, spin and lattice degrees of freedom on the spectral properties of the one-dimensional Hubbard-Holstein model

Cited by in corpus (4)

• Splitting the local Hilbert space: MPS-based approach to large local dimensions
• Unveiling Stripe-shaped Charge Density Modulations in Doped Mott Insulators
• Signatures of Quantum Phase Transitions in Driven Dissipative Spin Chains
• Summing Real Time Feynman Paths of Lattice Polaron with Matrix Product States