Phase diagram of the one-dimensional Holstein model of spinless fermions

TL;DR

This paper investigates the phase diagram of the one-dimensional Holstein model of spinless fermions using a novel DMRG variant, accurately identifying the metal-insulator transition and characterizing the transition as Kosterlitz-Thouless.

Contribution

It introduces a new DMRG approach to study the Holstein model and precisely maps the phase boundary across different regimes.

Findings

Phase boundary matches strong coupling theory in anti-adiabatic regime

Consistent with renormalisation group in adiabatic regime

Identifies Kosterlitz-Thouless transition via Luttinger parameters

Abstract

The one-dimensional Holstein model of spinless fermions interacting with dispersionless phonons is studied using a new variant of the density matrix renormalisation group. By examining various low-energy excitations of finite chains, the metal-insulator phase boundary is determined precisely and agrees with the predictions of strong coupling theory in the anti-adiabatic regime and is consistent with renormalisation group arguments in the adiabatic regime. The Luttinger liquid parameters, determined by finite-size scaling, are consistent with a Kosterlitz-Thouless transition.