One of the major theoretical challenges in high-Tc superconductivity is to first reproduce the observed phase diagrams that display the monotonously decreasing pseudogap temperature T* and the dome-shaped superconducting phase transition temperature Tc in the plane of temperature vs. hole concentration. Earlier Lee and Salk [J. Korean Phys. Soc. 37, 545 (2000); Phys. Rev. B 64, 052501 (2001)] reported a successful reproduction of the phase diagram by providing a realistic gauge theoretic [SU(2)/U(1)] slave-boson approach to the t - J Hamiltonian. Most recently, we [S.-H. S. Salk, Quantum Studies: Mathematics and Foundations 5, 149 (2018)] presented a comprehensive discussion on both the SU(2) and the U(1) approaches from which one can readily understand the intimate relationship between the two formalisms and discussed that both approaches can lead to room-temperature superconductivity with suitably high values of the antiferromagnetic coupling constant J, owing to the demonstration of identical physical propensities, i.e., the higher the J is, the higher the superconducting phase transition temperature Tc is. Here, we discuss hither-to-unreported detailed numerical computations of the phase diagrams by varying the values of J by using the U(1) gauge slave-boson approach to the t − J Hamiltonian. For the sake of testing convergence, we vary the unit-cell lattice sizes from 10 × 10 to a sufficiently large size of 50 × 50. We find that even a small square lattice size of 20 × 20 is seen to show reliable agreement with the results for higher lattice sizes while the 50 × 50 lattice size displays complete convergence in both T*and Tc. In addition, we present a physical analysis of the structure of the high-Tc phase diagram, focusing on the role of the spin pairing order in association with the interplay between the pseudo-gap (spin gap) temperature and the bose-condensation temperature/dome-shaped superconducting phase transition temperature.

中文翻译：

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高温超导性的详细数值分析和高温相图的物理分析基于对 t − J 哈密顿量的 U(1) Slave-Boson 方法

高温超导的主要理论挑战之一是首先重现观察到的相图，该图显示在温度与空穴浓度平面内单调降低的赝隙温度 T* 和圆顶形超导相变温度 Tc。较早的 Lee 和 Salk [J. 韩国物理 社会。37, 545 (2000); 物理。Rev. B 64, 052501 (2001)] 报道了通过为 t-J 哈密顿量提供现实规范理论 [SU(2)/U(1)] 从属玻色子方法，成功复制了相图。最近，我们 [S.-HS Salk, Quantum Studies: Mathematics and Foundations 5, 149 (2018)] 对 SU(2) 和 U(1) 方法进行了全面的讨论，从中可以很容易地理解两种形式主义之间的密切关系，并讨论了这两种方法都可以适当地导致室温超导反铁磁耦合常数 J 值高，这是由于证明了相同的物理特性，即 J 越高，超导相变温度 Tc 越高。在这里，我们通过对 t - J 哈密顿量使用 U(1) 规范从玻色子方法来改变 J 的值，讨论迄今为止尚未报道的相图的详细数值计算。为了测试收敛性，我们将单元格尺寸从 10 × 10 改变到足够大的 50 × 50 尺寸。我们发现，即使是 20 × 20 的小方形晶格尺寸也显示出与更高晶格尺寸的结果可靠一致，而 50 × 50 晶格尺寸在 T* 和 Tc 中显示完全收敛。此外，我们对高 Tc 相图的结构进行了物理分析，重点关注自旋配对顺序与伪间隙（自旋间隙）温度和玻色凝聚温度之间的相互作用的作用。圆顶形超导相变温度。