We present a new method to treat the two-dimensional (2D) Hubbard model for parameter regimes which are relevant for the physics of the high-$T_c$ superconducting cuprates. Unlike previous attempts to attack this problem, our new approach takes into account all fluctuations in different channels on equal footing and is able to treat reasonable large lattice sizes up to 32x32. This is achieved by the following three-step procedure: (i) We transform the original problem to a new representation (dual fermions) in which all purely local correlation effects from the dynamical mean field theory are already considered in the bare propagator and bare interaction of the new problem. (ii) The strong $1/(i\nu {)}^2$ decay of the bare propagator allows us to integrate out all higher Matsubara frequencies besides the lowest using low order diagrams. The new effective action depends only on the two lowest Matsubara frequencies which allows us to, (iii) apply the two-particle self-consistent parquet formalism, which takes into account the competition between different low-energy bosonic modes in an unbiased way, on much finer momentum grids than usual. In this way, we were able to map out the phase diagram of the 2D Hubbard model as a function of temperature and doping. Consistently with the experimental evidence for hole-doped cuprates and previous dynamical cluster approximation calculations, we find an antiferromagnetic region at low-doping and a superconducting dome at higher doping. Our results also support the role of the van Hove singularity as an important ingredient for the high value of $T_c$ at optimal doping. At small doping, the destruction of antiferromagnetism is accompanied by an increase of charge fluctuations supporting the scenario of a phase separated state driven by quantum critical fluctuations.

中文翻译：

---

二维Hubbard模型的双重拼花方案：以高动量分辨率模拟高速率的低能物理

我们提出了一种新的方法来处理二维（2D）Hubbard模型中与高物理场相关的参数范围${Ť}_C$超导铜酸盐。与以前尝试解决此问题的尝试不同，我们的新方法考虑到了在相同的立足点上不同通道中的所有波动，并且能够处理高达32x32的合理大晶格尺寸。这可以通过以下三步过程来实现：（i）我们将原始问题转换为新的表示形式（双费米子），其中在裸机传播器和裸机交互中已经考虑了来自动力学平均场理论的所有纯局部相关效应新问题。（ii）强者$\mathrm{1个}/（\mathrm{一世}\nu {）}^2$裸机传播的衰减使我们能够使用低阶图将最低的松原频率进行积分。新的有效措施仅取决于两个最低的松原频率，这使我们能够：（iii）应用两粒子自洽拼花形式，这以无偏的方式考虑了不同低能玻色模式之间的竞争。比平常要好得多的动量网格。通过这种方式，我们能够根据温度和掺杂绘制出二维Hubbard模型的相图。与掺杂空穴的铜酸盐的实验证据和先前的动态簇近似计算一致，我们发现低掺杂时存在反铁磁区域，而高掺杂时则存在超导圆顶。${Ť}_C$以最佳掺杂。在少量掺杂时，反铁磁性的破坏伴随着电荷波动的增加，从而支持了由量子临界波动驱动的相分离态的情形。