t-J模型重整化平均场论的统计一致变分方法：成对态的临界空穴浓度
A statistically consistent variational approach to the renormalized mean-field theory of the t-J model: critical hole concentrations for a paired state
摘要：
最近，Fukushima [Phys. Rev. B \textbf{78} 115105（2008）]提出了用于t-J模型的Gutzwiller近似的系统推导。在本文中，使用这种方法，我们构建了一个有效的单粒子哈密顿量，这导致了重整化平均场论（RMFT）。我们还使用我们最近提出的方法，并基于最大熵原理（MaxEnt），这反过来又产生了一致的统计描述的问题。以非磁性超导d波共振价键（dRVB）和正常交错磁通（SF）解为例，比较了两种Gutzwiller重整化方案，即Fukushima提出的方案和Sigrist等人[Phys. Rev. \textbf{49}，12058（1994）]所采用的方案。我们还面临的结果来自我们的变分解决方案的自洽条件内置，与那些非变分方法的基础上的Bogoliubov-德Gennes自洽方程。结合本变分方法与新的重整化方案（从福岛的工作）提供，$t/J =3$，上临界空穴浓度$x_{c} \approx 0.27$的d波超导性的消失。此外，获得了最佳掺杂的空穴浓度$x \approx 0.125$。这些结果与高$T_c$超导铜氧化物的实验结果基本一致。
英文摘要：
Recently, Fukushima [Phys. Rev. B \textbf{78} 115105 (2008)] proposed a systematic derivation of the Gutzwiller approximation for the t-J model. In the present paper, using this approach we construct an effective single-particle Hamiltonian, which leads to a renormalized mean-field theory (RMFT). We also use the method proposed by us recently and based on the maximum entropy principle (MaxEnt), which in turn, yields a consistent statistical description of the problem. On the examples of non-magnetic superconducting d-wave resonating valence bond (dRVB) and normal staggered-flux (SF) solutions, we compare two selections of the Gutzwiller renormalization schemes, i.e. the one proposed by Fukushima with that used earlier by Sigrist et al. [Phys. Rev. B \textbf{49}, 12 058 (1994)]. We also confront the results coming from our variational solutions with the self-consistency conditions build in, with those of the non-variational approach based on the Bogoliubov-de Gennes self-consistent equations. Combination of the present variational approach with the new renormalization scheme (taken from Fukushima's work) provides, for $t/J =3$, an upper critical hole concentration $x_{c} \approx 0.27$ for the disappearance of the d-wave superconductivity. Also, the hole concentration $x \approx 0.125$ is obtained for the optimal doping. These results are in rough accordance with experimental results for high-$T_c$ superconducting cuprates.
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