Doping evolution of spin and charge excitations in the Hubbard model

TL;DR

This study investigates how doping affects spin and charge excitations in the Hubbard model, revealing persistent correlations at high doping levels and a transition to a weakly correlated metallic state where RPA becomes valid.

Contribution

It provides a detailed analysis of the doping evolution of two-particle excitations in the Hubbard model, highlighting the limitations of RPA at intermediate dopings and the crossover to a weakly correlated phase.

Findings

Residual correlations persist up to 40% hole and 15% electron doping.

Single-particle correlations weaken rapidly with doping.

RPA becomes adequate in the weakly correlated metallic state.

Abstract

To shed light on how electronic correlations vary across the phase diagram of the cuprate superconductors, we examine the doping evolution of spin and charge excitations in the single-band Hubbard model using determinant quantum Monte Carlo (DQMC). In the single-particle response, we observe that the effects of correlations weaken rapidly with doping, such that one may expect the random phase approximation (RPA) to provide an adequate description of the two-particle response. In contrast, when compared to RPA, we find that significant residual correlations in the two-particle excitations persist up to $40\%$ hole and $15\%$ electron doping (the range of dopings achieved in the cuprates). These fundamental differences between the doping evolution of single- and multi-particle renormalizations show that conclusions drawn from single-particle processes cannot necessarily be applied to multi-particle excitations. Eventually, the system smoothly transitions via a momentum-dependent crossover into a weakly correlated metallic state where the spin and charge excitation spectra exhibit similar behavior and where RPA provides an adequate description.