Metallicity in the half-filled Holstein-Hubbard model

TL;DR

This study uses advanced numerical methods to analyze phase transitions in the one-dimensional Holstein-Hubbard model, revealing an extended metallic phase with distinct liquid states at weak coupling.

Contribution

It provides a detailed finite-size scaling analysis confirming the existence of an intervening metallic phase and characterizes its subphases at large phonon frequencies.

Findings

Identification of an extended metallic region in the phase diagram.

Discovery of Luttinger liquid and bipolaronic liquid subphases.

Confirmation of a metallic phase at weak electron-phonon coupling.

Abstract

We re-examine the Peierls insulator to Mott insulator transition scenario in the one-dimensional Holstein-Hubbard model where, at half-filling, electron-phonon and electron-electron interactions compete for establishing charge- and spin-density-wave states, respectively. By means of large-scale density-matrix renormalization group calculations we determine the spin, single-particle and two-particle excitation gaps and prove--in the course of a careful finite-size scaling analysis--recent claims for an intervening metallic phase in the weak-coupling regime. We show that for large phonon frequencies the metallic region is even more extended than previously expected, and subdivided into ordinary Luttinger liquid and bipolaronic liquid phases.