Phase diagram for the one-dimensional Hubbard-Holstein model: A density-matrix renormalization group study

TL;DR

This study maps the phase diagram of the 1D Hubbard-Holstein model using density-matrix renormalization group, revealing regions of metallic behavior and dominant pairing correlations under various doping and lattice conditions.

Contribution

It provides the first comprehensive phase diagram of the 1D Hubbard-Holstein model considering full parameter space using an improved DMRG method.

Findings

Identified a metallic phase with power-law decay of correlations.

Found that pairing correlations become dominant upon doping or lattice modification.

Mapped the phase diagram across different electron fillings and lattice structures.

Abstract

Phase diagram of the Hubbard-Holstein model in the coexistence of electron-electron and electron-phonon interactions has been theoretically obtained with the density-matrix renormalization group method for one-dimensional (1D) systems, where an improved warm-up (the recursive sweep) procedure has enabled us to calculate various correlation functions. We have examined the cases of (i) the systems half-filled by electrons for the full parameter space spanned by the electron-electron and electron-phonon coupling constants and the phonon frequency, (ii) non-half-filled system, and (iii) trestle lattice. For (i), we have detected a region where both the charge and on-site pairing correlations decay with power-laws in real space, which suggests a metallic behavior. While pairing correlations are not dominant in (i), we have found that they become dominant as the system is doped in (ii), or as the electronic band structure is modified (with a broken electron-hole symmetry) in (iii) in certain parameter regions.