Towards effective models for low-dimensional cuprates: From ground-state Hamiltonian reconstruction to spectral functions

Understanding which minimal effective model captures the essential physics of cuprates is a key step towards unraveling the mechanism behind high- <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:msub> <a:mi>T</a:mi> <a:mi>c</a:mi> </a:msub> </a:math> superconductivity. Recent measurements of the dynamical spin structure factor (DSF) in cuprate ladder compounds have indicated the presence of an additional, attractive term in the single-band Hubbard model, potentially originating from electron-phonon interactions. Here, we demonstrate that similar DSF features can also be captured by <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mi>t</b:mi> <b:mtext>−</b:mtext> <b:mi>J</b:mi> </b:mrow> </b:math> descriptions with a smaller attractive term. Motivated by this observation, we systematically investigate the strength and origin of different contributions to the single-band Hamiltonians by downfolding either from the three-band Emery model or the electron-phonon coupled Hubbard-Holstein model. For one-dimensional systems, we find that the extended versions of both single-band descriptions can reproduce the experimentally observed DSF signatures. Finally, we extend our analysis to two dimensions by comparing two-hole correlation functions for the different single-band models. Our results provide new insights into the long-standing question of which single-band Hamiltonian can capture the essential physics of cuprates.