哈伯德模型中的阻挫电子液体
Frustrated electron liquids in the Hubbard model
摘要：
在不存在序参量的约束Hilbert空间中研究了哈伯德模型的基态.将电子的自能分解为单位和多位自能。将单格点自能的计算映射为Anderson模型的自洽求解问题。当明确考虑电子库时，证明了即使多位点自能是反常的，单位点自能也是正常费米液体的自能。因此，在最高单点近似（S^3 A）下，基态是正常的费米液体。在强耦合区，费米液体在S^3A中被近藤效应稳定，并在S^3A之外被超交换相互作用的福克型项或共振价键（RVB）机制进一步稳定。在海森堡模型中，稳定的费米液体和RVB自旋液体一样受挫。它是一个相关的未微扰态，可以用来研究正常或反常的费米液体，以及用近藤晶格理论研究整个希尔伯特空间中的有序态。即使考虑比福克型项更高阶的多位项，基态也不能是莫特绝缘体。它可以仅仅是一个无带隙半导体，即使多位点自能是如此反常，以至于它在化学势上是发散的。莫特绝缘体只能作为高温相。
英文摘要：
The ground state of the Hubbard model is studied within the constrained Hilbert space where no order parameter exists. The self-energy of electrons is decomposed into the single-site and multisite self-energies. The calculation of the single-site self-energy is mapped to a problem of self-consistently determining and solving the Anderson model. When an electron reservoir is explicitly considered, it is proved that the single-site self-energy is that of a normal Fermi liquid even if the multisite self-energy is anomalous. Thus, the ground state is a normal Fermi liquid in the supreme single-site approximation (S^3A). In the strong-coupling regime, the Fermi liquid is stabilized by the Kondo effect in the S^3A and is further stabilized by the Fock-type term of the superexchange interaction or the resonating-valence-bond (RVB) mechanism beyond the S^3A. The stabilized Fermi liquid is frustrated as much as an RVB spin liquid in the Heisenberg model. It is a relevant unperturbed state that can be used to study a normal or anomalous Fermi liquid and an ordered state in the whole Hilbert space by Kondo lattice theory. Even if higher-order multisite terms than the Fock-type term are considered, the ground state cannot be a Mott insulator. It can be merely a gapless semiconductor even if the multisite self-energy is so anomalous that it is divergent at the chemical potential. A Mott insulator is only possible as a high temperature phase.
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