Doping evolution of charge and spin excitations in two-leg Hubbard ladders: comparing DMRG and RPA+FLEX results

TL;DR

This study compares DMRG and RPA+FLEX methods to analyze charge and spin excitations in two-leg Hubbard ladders, revealing RPA+FLEX's effectiveness at weak to intermediate couplings and its limitations at stronger interactions.

Contribution

The paper demonstrates that RPA+FLEX accurately captures magnetic responses in doped two-leg Hubbard ladders at weak to intermediate couplings, validated against DMRG results.

Findings

RPA+FLEX reproduces main magnetic features at weak to intermediate U.

DMRG shows gapped spin excitations at large momentum transfer, not captured by RPA+FLEX.

RPA+FLEX's accuracy diminishes for charge response at strong coupling and low doping.

Abstract

We study the magnetic and charge dynamical response of a Hubbard model in a two-leg ladder geometry using the density matrix renormalization group (DMRG) method and the random phase approximation within the fluctuation-exchange approximation (RPA+FLEX). Our calculations reveal that RPA+FLEX can capture the main features of the magnetic response from weak up to intermediate Hubbard repulsion for doped ladders, when compared with the numerically exact DMRG results. However, while at weak Hubbard repulsion both the spin and charge spectra can be understood in terms of weakly-interacting electron-hole excitations across the Fermi surface, at intermediate coupling DMRG shows gapped spin excitations at large momentum transfer that remain gapless within the RPA+FLEX approximation. For the charge response, RPA+FLEX can only reproduce the main features of the DMRG spectra at weak coupling and high doping levels, while it shows an incoherent character away from this limit. Overall, our analysis shows that RPA+FLEX works surprisingly well for spin excitations at weak and intermediate Hubbard $U$ values even in the difficult low-dimensional geometry such as a two-leg ladder. Finally, we discuss the implications of our results for neutron scattering and resonant inelastic x-ray scattering experiments on two-leg ladder cuprate compounds.