Static versus dynamic fluctuations in the one-dimensional extended Hubbard model

TL;DR

This study compares static and dynamic lattice effects on correlations in the one-dimensional extended Hubbard model, revealing how lattice coupling influences charge, spin, and bond order through quantum Monte Carlo simulations.

Contribution

It demonstrates the impact of static versus dynamic lattice distortions on phase correlations in the extended Hubbard model using world-line quantum Monte Carlo methods.

Findings

Static lattice distortion enhances charge density wave correlations.

Dynamic lattice coupling induces spontaneous charge asymmetry.

Sharp crossovers in energy components mark phase boundaries.

Abstract

The extended Hubbard Hamiltonian is a widely accepted model for uncovering the effects of strong correlations on the phase diagram of low-dimensional systems, and a variety of theoretical techniques have been applied to it. In this paper the world-line quantum Monte Carlo method is used to study spin, charge, and bond order correlations of the one-dimensional extended Hubbard model in the presence of coupling to the lattice. A static alternating lattice distortion (the ionic Hubbard model) leads to enhanced charge density wave correlations at the expense of antiferromagnetic order. When the lattice degrees of freedom are dynamic (the Hubbard-Holstein model), we show that a similar effect occurs even though the charge asymmetry must arise spontaneously. Although the evolution of the total energy with lattice coupling is smooth, the individual components exhibit sharp crossovers at the phase boundaries. Finally, we observe a tendency for bond order in the region between the charge and spin density wave phases.