Spin-phonon effects in the two-band Hubbard model

Mustansir Barma, Robert A. Bari

Hannah Lange, Tizian Blatz, Ulrich Schollwöck +2 more

Understanding which minimal effective model captures the essential physics of cuprates is a key step towards unraveling the mechanism behind high- T c 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 t − J 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.

M. Gulácsi, Annette Bussmann‐Holder, A. R. Bishop

D. Schmeltzer, A. R. Bishop

Using the slave boson method for the 1-band Hubbard model, we derive an effective Hamiltonian in terms of charge and spin variables. For large values of the Hubbard U we recover the standard t-J model. For smaller values of U the range of interaction between the spin and charge variables is increased. We also consider the effect of an onsite electron-phonon interaction and show that the effect of integrating the double occupancy and the integration of phonons is in general not additive.

Anh Tuan Hoang, Toan Thang Nguyen, Ngoc Thuan Nguyen

Yury Petrov, T. Egami

The effective two-band $t\ensuremath{-}J$ Hamiltonian for holes in Cu-O planes of cuprates is obtained from the three-band Hubbard Hamiltonian. In this model a doped oxygen hole together with two neighboring copper holes is treated as a composite spin-$\frac{1}{2}$ three-sites particle. The model is studied by exact diagonalization in a ${\mathrm{Cu}}_{16}{\mathrm{O}}_{32}$ square cluster. Both binding energy and hole-hole correlation function indicate that two holes bind together for $J/t>0.11$ and are predominantly located on the next-nearest oxygen sites in the same Cu-O chain. Electron-phonon interaction is studied in the adiabatic phonons approximation. Copper (\ensuremath{\pi},0) ``half-breathing'' mode is shown to couple strongly to doped holes and increase the hole-hole correlation as well as the binding energy. These results are compared with experimental data.