Theory of Resonating Quantum Fluctuations in a Fermion System -- Resonating Hartree-Fock Approximation--
Theory of Resonating Quantum Fluctuations in a Fermion System -- Resonating Hartree-Fock Approximation--
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费米子系统中共振量子涨落理论——共振 Hartree-Fock 近似——
DOI：
10.1143/ptp.80.417
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发表时间：
1988
影响因子：
--
通讯作者：
H. Fukutome
中科院分区：
文献类型：
--
作者：
H. Fukutome
我们发展了一个新的一般理论，用于研究费米子多体系统中的大量子涨落，这种涨落不能用Hartree·Fock基态附近的涨落来描述，而是由不同关联结构的共振引起的.我们从酉群上费米子系统的精确相干态表示开始。我们证明了相干态表象中的哈密顿量与Hartree·Fock能量泛函有着密切的联系。由此，我们可以导出一种新的近似，称为共振Hartree·Fock近似。在这种近似中，一个态可以用具有不同关联结构的非正交斯莱特确定子的叠加来近似。我们导出了确定共振Hartree·Fock波函数的变分方程。我们证明了简并破缺对称性斯莱特行列式之间的共振可以部分地恢复对称性。讨论了共振Hartree·Fock波函数中试探斯莱特行列式的选取问题。我们认为，在HF基态长程有序中产生的代表局域缺陷的斯莱特行列式（如孤子、极化子和呼吸子）的共振可能是凝聚态系统中大量子涨落的最重要内容.
We develop a new general theory for large quantum fluctuations in a Fermion many·body system that cannot be described by fluctuations around the Hartree·Fock ground state but arises from resonance of different correlation structures. We start with an exact coherent state representation of a Fermion system on a unitary group. We show that the Hamiltonian in the coherent state representation has a close connection with the Hartree·Fock energy functional. From this, we can derive a new approximation called the resonating Hartree·Fock approximation in which a state is approximated by a superposition of non· orthogonal Slater deterrp.inants with different correlation structures. We derive the variation equations to determine a resonating Hartree· Fock wavefunction. We show that the resonance between degenerate broken symmetry Slater determinants may partially recover the symmetry. We discuss how to choose trial Slater determinants in a resonating Hartree· Fock wavefunction. We suggest that resonance of Slater determinants representing localized defects, such as solitons, polarons and breathers, produced in the long range order of the HF ground state may be the most important content of large quantum fluctuations in condensed matter systems.