Ground state of a general electron-phonon Hamiltonian is a spin singlet.
Ground state of a general electron-phonon Hamiltonian is a spin singlet.
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一般电子声子哈密顿量的基态是自旋单线态。
DOI：
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发表时间：
1994
期刊：
影响因子：
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通讯作者：
Lieb
中科院分区：
文献类型：
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作者：
Freericks;Lieb
证明了一类非常一般的电子-声子哈密顿子的多体基态包含自旋单重态（对于有限晶格上的偶数电子）。声子以两种不同的方式与电子系统相互作用——与局部电子电荷相互作用，以及电子跳跃哈密顿量与声子坐标的函数依赖。声子势能可能包含非调和项，电子-声子耦合和跳矩阵元素可能是声子坐标的非线性函数。如果假设跳跃哈密顿量与声子坐标无关，则基态也被证明是唯一的，这意味着不存在基态水平交叉，基态能量是哈密顿量中参数的解析函数。特别地，在有限系统中，任何自捕获跃迁都是平滑的交叉，不伴随着基态的非解析变化。自旋单线态定理适用于Su-Schrieffer-Heeger模型，自旋单线态定理和唯一性定理作为特殊情况适用于Holstein模型和吸引Hubbard模型。这些结果在所有维度上都成立——甚至在没有周期晶格结构的一般图上也是如此。
The many-body ground state of a very general class of electron-phonon Hamiltonians is proven to contain a spin singlet (for an even number of electrons on a finite lattice). The phonons interact with the electronic system in two different ways---there is an interaction with the local electronic charge and there is a functional dependence of the electronic hopping Hamiltonian on the phonon coordinates. The phonon potential energy may include anharmonic terms, and the electron-phonon couplings and the hopping matrix elements may be nonlinear functions of the phonon coordinates. If the hopping Hamiltonian is assumed to have no phonon coordinate dependence, then the ground state is also shown to be unique, implying that there are no ground-state level crossings, and that the ground-state energy is an analytic function of the parameters in the Hamiltonian. In particular, in a finite system any self-trapping transition is a smooth crossover not accompanied by a nonanalytical change in the ground state. The spin-singlet theorem applies to the Su-Schrieffer-Heeger model and both the spin-singlet and uniqueness theorems apply to the Holstein and attractive Hubbard models as special cases. These results hold in all dimensions --- even on a general graph without periodic lattice structure.