Quantum phase transition in a 1D transport model with boson affected hopping: Luttinger liquid versus charge-density-wave behavior

TL;DR

This paper investigates a 1D fermion-boson model using advanced DMRG techniques, revealing a quantum phase transition between metallic and insulating states characterized by various physical properties.

Contribution

It introduces a refined pseudo-site DMRG method to analyze a general fermion-boson model and maps out its ground-state phase diagram including a metal-insulator transition.

Findings

Identifies a quantum phase transition at half-filling

Characterizes metallic and insulating regimes with multiple physical quantities

Provides detailed phase diagram for the model

Abstract

We solve a very general two-channel fermion-boson model describing charge transport within some background medium by means of a refined pseudo-site density matrix renormalization group (DMRG) technique. Performing a careful finite-size scaling analysis, we determine the ground-state phase diagram and convincingly prove that the model exhibits a metal-insulator quantum phase transition for the half-filled band case. In order to characterize the metallic and insulating regimes we calculate besides the local particle densities and fermion-boson correlation functions, the kinetic energy, the charge structure factor, the Luttinger liquid charge exponent and the single-particle excitation gap for a one-dimensional infinite system.