Interplay of charge, spin and lattice degrees of freedom on the spectral properties of the one-dimensional Hubbard-Holstein model

TL;DR

This study uses tDMRG to analyze the spectral properties of the 1D Hubbard-Holstein model, revealing how charge, spin, and lattice interactions influence the spectrum across different electron-phonon coupling regimes.

Contribution

It introduces a combined numerical and analytical approach to understand spectral features in the Hubbard-Holstein model, especially the transition to a spinless polaronic liquid at strong coupling.

Findings

Phonons interact mainly with charge, not spin, at weak to intermediate coupling.

Strong coupling leads to a spinless polaronic liquid with multiple phonon-related spectral peaks.

Spectral features can be interpreted through a convolution of charge, spin, and lattice contributions.

Abstract

We calculate the spectral function of the one dimensional Hubbard-Holstein model using the time dependent Density Matrix Renormalization Group (tDMRG), focusing on the regime of large local Coulomb repulsion, and away from electronic half-filling. We argue that, from weak to intermediate electron-phonon coupling, phonons interact only with the electronic charge, and not with the spin degrees of freedom. For strong electron-phonon interaction, spinon and holon bands are not discernible anymore and the system is well described by a spinless polaronic liquid. In this regime, we observe multiple peaks in the spectrum with an energy separation corresponding to the energy of the lattice vibrations (i.e., phonons). We support the numerical results by introducing a well controlled analytical approach based on Ogata-Shiba's factorized wave-function, showing that the spectrum can be understood as a convolution of three contributions, originating from charge, spin, and lattice sectors. We recognize and interpret these signatures in the spectral properties and discuss the experimental implications.