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arXiv 1502.04799cond-mat.str-el
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变分理论中的Drude权、超导权和Mott跃迁

Drude and Superconducting Weights and Mott Transitions in Variation Theory

Shun Tamura, Hisatoshi Yokoyama

备注：
11pages, 14figures
发表信息：
J. Phys. Soc. Jpn. 84, 064707 (2015)
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摘要：

德鲁德重量（$D$）是区分金属与绝缘体的有用量度。然而，$D$长期以来没有被变分理论合理地估计，因为Millis和Coppermith [Phys.Rev.B43（1991）13770]指出，变分波函数$Ψ_Q$，包括莫特跃迁的关键成分（双光子-holon结合效应），即使在莫特绝缘区也产生正的$D$（即金属）。我们认为，要得到正确的$D$，虚部必须存在于波函数。通过在$Ψ_Q$中引入与组态相关的相位因子${\cal P}_θ$，成功地用$D$（$D=0$ for $U>U_{\rm c}$）表示了正常态和$d$波对态的Mott跃迁，从而解决了Millis和Coppersmith问题.一般来说，${\cal P}_θ$在描述莫特物理体系中的载流态时起着关键作用。另一方面，我们表明，使用微扰理论，一个身体（平均场）的波函数的一部分应该是复杂的带绝缘体，如超立方晶格中的反铁磁状态。

英文摘要：

Drude weight ($D$) is a useful measure to distinguish a metal from an insulator. However, $D$ has not been justifiably estimated by the variation theory for long, since Millis and Coppersmith [Phys. Rev. B 43 (1991) 13770] pointed out that a variational wave function $Ψ_Q$, which includes the key ingredient (doublon-holon binding effect) for a Mott transition, yields a positive $D$ (namely metallic) even in the Mott-insulating regime. We argue that, to obtain a correct $D$, an imaginary part must exist in the wave function. By introducing a configuration-dependent phase factor ${\cal P}_θ$ to $Ψ_Q$, Mott transitions are successfully represented by $D$ ($D=0$ for $U>U_{\rm c}$) for a normal and $d$-wave pairing states; thereby, the problem of Millis and Coppersmith is settled. Generally, ${\cal P}_θ$ plays a pivotal role in describing current-carrying states in regimes of Mott physics. On the other hand, we show using a perturbation theory, the one-body (mean-field) part of the wave function should be complex for band insulators such as antiferromagnetic states in hypercubic lattices.

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