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

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.

9 pages, 8 figures, submitted to Physical Review B

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• Particle-hole asymmetry in the dynamical spin and charge structure factors of the corner-shared one-dimensional cuprates
• Theoretical study of the spin and charge dynamics of two-leg ladders as probed by resonant inelastic x-ray scattering
• Robust superconducting correlation against inter-site interactions in the extended two-leg Hubbard ladder
• Spectroscopic signatures of next-nearest-neighbor hopping in the charge and spin dynamics of doped one-dimensional antiferromagnets
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• Root-N Krylov-space correction-vectors for spectral functions with the density matrix renormalization group
• Beyond-Hubbard pairing in a cuprate ladder
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