Neural-quantum-state based downfolding of the three-band Emery model for cuprates and nickelates

Summary

This paper employs neural quantum states, in particular hidden fermion determinant states (HFDS), to perform a scalable variational study of the three-band Emery model for CuO₂/NiO₂ planes in cuprates and nickelates. The authors first benchmark against matrix product states on width-two geometries and then simulate fully two-dimensional systems up to 10×10 unit cells (300 sites), characterizing the momentum-space distribution of dopants and finding an electron-hole dichotomy similar to that observed in cuprate experiments. The study further downfolds the three-band model to an effective single-band description by constructing interacting Wannier functions, with parameters covering the cuprate charge-transfer regime, the nickelate Hubbard-Mott regime, and scans of the charge-transfer gap. The results show that the effective model deviates significantly from the usual Fermi-Hubbard model: U/t is enhanced, some parameters exhibit pronounced doping dependence, and important terms beyond the conventional Hubbard model emerge, most notably the density-assisted hopping t_n; moreover, t_n makes the largest contribution to particle-hole asymmetry, rather than next-nearest-neighbor hopping. The effective parameters depend sensitively on the charge-transfer energy, doping, and interaction ratio. The conclusion is that HFDS is an efficient tool for studying the two-dimensional Emery model, and that a single-band description may need to include new interaction terms generated by the underlying multiband model.

Materials

• cuprates
• infinite-layer nickelates
• copper-oxide layers
• nickel-oxide layers
• CuO₂ planes

Methods

• Neural quantum states (NQS)
• Hidden Fermion Determinant States (HFDS)
• Matrix product states (MPS)
• Density-matrix renormalization group (DMRG)
• Convolutional neural networks (CNNs)
• Interacting Wannier functions
• Downfolding
• Variational optimization
• Symmetry-averaging

Keywords

• high temperature superconductivity
• three band emery model
• single band fermi hubbard model
• electron hole asymmetry
• nodal antinodal dichotomy
• charge transfer gap
• density assisted hopping
• particle hole asymmetry
• charge transfer regime
• hubbard mott regime
• superconducting critical temperature
• zhang rice singlets
• momentum space distribution of dopants
• fermi arc

Highlights

• To our knowledge, this is the first time that NQS are employed for a three-band study.
• Despite the apparent increase in complexity, the number of simulated fermions is not increased by a factor of three; instead, the dimension of the determinant remains of the same order as in single-band models, rendering its evaluation computationally comparable to that of the corresponding single-band ansätze.
• Our NQS provide competitive energies with a substantially smaller number of variational parameters while extending naturally to geometries beyond the quasi-one-dimensional regime.
• The data for different system sizes are nearly indistinguishable, indicating that finite-size effects are small.
• Including V_pd in the downfolding significantly enhances t_n and moreover generates additional equal-spin density terms that are not present for V_pd=0.
• The electron-hole asymmetry is captured by t_n, rather than by assigning different signs to t'.
• This procedure follows Ref. [32], but we extend the analysis to systematic Emery parameter and doping scans.

Conclusions

• HFDS provide an efficient variational description of the copper- and nickel-oxide layers of cuprate and nickelate superconductors that goes beyond the usually considered single-band Fermi-Hubbard model: the three-band Emery model.
• The favorable scaling of HFDS enables accurate calculations on square lattices of up to 10×10 unit cells, establishing NQS as a practical route to studying the ground state of the Emery model on large two-dimensional systems.
• The simulations reveal a clear asymmetry between electron and hole doping in momentum space, which is qualitatively consistent with ARPES experiments in cuprates.
• The systematic downfolding of the correlated three-band ground state to an effective single-band description finds sizable contributions beyond the bare Fermi-Hubbard model.
• The effective model significantly deviates from the usual Fermi-Hubbard model: the typical ratio U/t is enhanced, some parameters experience a significant doping dependence, and sizable terms beyond the conventional Hubbard model are present, most notably a density-assisted hopping t_n.
• In all effective models, t_n has the largest contribution to particle-hole asymmetry, rather than next-nearest-neighbor hopping contributions.
• The effective parameters sensitively depend on the charge-transfer energy, doping, and interaction ratios.
• The charge-transfer energy has a particularly strong impact on the spatial extent of the interacting Wannier orbitals and, consequently, on the effective hopping and interaction strengths.
• Single-band descriptions can require interaction terms generated by the underlying multi-band models.

Main claims

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Workflow

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