摘要
本文利用神经量子态，特别是隐藏费米子行列式态（HFDS），对铜氧化物与镍氧化物中铜氧/镍氧面的三带Emery模型开展可扩展变分研究。作者先在宽度为二的几何上与矩阵乘积态基准比较，随后模拟至10×10元胞（300格点）的完全二维体系，刻画掺杂子的动量空间分布并发现类似铜氧化物实验的电子-空穴二分性。研究进一步通过构造相互作用Wannier函数将三带模型下折叠为有效单带描述，参数覆盖铜氧化物电荷转移区、镍氧化物Hubbard-Mott区以及电荷转移能隙扫描。结果表明有效模型显著偏离通常Fermi-Hubbard模型：U/t增强、部分参数具显著掺杂依赖，并出现常规Hubbard模型之外的重要项，尤以密度辅助跃迁tn最为突出；且tn对粒子-空穴不对称性的贡献最大，而非次近邻跃迁。有效参数敏感依赖于电荷转移能、掺杂和相互作用比。结论是HFDS是研究二维Emery模型的高效工具，单带描述可能需要包含由底层多带模型产生的新相互作用项。
材料
- cuprates
- infinite-layer nickelates
- copper-oxide layers
- nickel-oxide layers
- CuO2 planes
方法
- 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
关键词
- 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
亮点
- 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 Vpd in the downfolding significantly enhances tn and moreover generates additional equal-spin density terms that are not present for Vpd=0.
- The electron-hole asymmetry is captured by tn, 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.
结论
- 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 tn.
- In all effective models, tn 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.
主要论断
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研究流程
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