The isotope effect in the Hubbard model with local phonons

TL;DR

This study investigates the isotope effect in the 2D Hubbard model with Holstein phonons, revealing its dependence on electron-phonon coupling, doping, and phonon frequency, with implications for understanding cuprate superconductors.

Contribution

It provides a detailed analysis of the isotope effect in the Hubbard-Holstein model, highlighting the role of polaronic effects and doping in the isotope dependence of various physical properties.

Findings

Large positive isotope effect on superconducting temperature at strong EP coupling

Significant isotope effect observed in low-energy density of states and charge spectrum

Negligible isotope effect in pseudogap and antiferromagnetic properties at small doping

Abstract

The isotope effect (IE) in the two-dimensional Hubbard model with Holstein phonons is studied using the dynamical cluster approximation with quantum Monte Carlo. At small electron-phonon (EP) coupling the IE is negligible. For larger EP coupling there is a large and positive IE on the superconducting temperature that decreases with increasing doping. A significant IE also appears in the low-energy density of states, kinetic energy and charge excitation spectrum. A negligible IE is found in the pseudogap and antiferromagnetic (AF) properties at small doping whereas the AF susceptibility at intermediate doping increases with decreasing phonon frequency $\omega_0$. This IE stems from increased polaronic effects with decreasing $\omega_0$. A larger IE at smaller doping occurs due to stronger polaronic effects determined by the interplay of the EP interaction with stronger AF correlations. The IE of the Hubbard-Holstein model exhibits many similarities with the IE measured in cuprate superconductors.