We present a way to partly reincorporate the effects of the localized bonding electrons on the dynamics of their itinerant counterparts in Hubbard-like Hamiltonians. This is done by relaxing the constraint that the former should be entirely frozen in the chemical bonds between the underlying lattice sites through the employment of a Born-Oppenheimer-like ansatz for the wave function of the whole electronic system. Accordingly, the latter includes itinerant as well as bonding electron coordinates. Going beyond the adiabatic approximation, we show that the net effect of virtual transitions of bonding electrons between their ground and excited states is to furnish the itinerant electrons with an effective interelectronic momentum-momentum interaction. Although we have applied these ideas to the specific case of rings, our assumptions can be generalized to higher-dimensional systems sharing the required properties of which we have made use herein.

中文翻译：

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相关电子系统中的有效动量-动量耦合

我们提出了一种方法，以部分重新结合局部键合电子对其在类似哈伯德式哈密顿量中的巡回对应物的动力学的影响。这是通过放宽前者应通过将类Born-Oppenheimer的ansatz用于整个电子系统的波函​​数而完全冻结在下面晶格位点之间的化学键中的约束来完成的。因此，后者包括流动剂以及键合电子坐标。超越绝热近似，我们证明了键合电子在其基态和激发态之间的虚拟跃迁的净效应是为流动电子提供有效的电子间动量-动量相互作用。尽管我们已将这些想法应用于特定的戒指情况，