# Effective Hamiltonian for cuprate superconductors derived from multi-scale ab initio scheme with level renormalization

## TL;DR

This paper develops refined effective Hamiltonians for cuprate superconductors using an advanced multi-scale ab initio scheme, improving accuracy in electronic structure predictions and aiding understanding of superconductivity mechanisms.

## Contribution

The paper introduces improved multi-scale ab initio effective Hamiltonians for cuprates, surpassing previous approximations and better matching experimental data.

## Key findings

- Charge gap and magnetic moments agree with experiments
- Refined Hamiltonians clarify electronic structures
- Enhanced treatment of interband interactions

## Abstract

Three-types (three-band, two-band and one-band) of effective Hamiltonians for the HgBa$_2$CuO$_4$ and three-band effective Hamiltonian for La$_2$CuO$_4$ are derived beyond the level of the constrained-GW approximation combined with the self-interaction correction (cGW-SIC) derived in Hirayama et al. Phys. Rev. B 98, 134501 (2018) by improving the treatment of the interband Hartree energy. The charge gap and antiferromagnetic ordered moment show good agreement with the experimental results when the present effective Hamiltonian is solved, indicating the importance of the present refinement. The obtained Hamiltonians will serve to clarify the electronic structures of these copper oxide superconductors and to elucidate the superconducting mechanism.