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arXiv 0908.1225cond-mat.str-el
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掺杂量子铁磁体的微观模型与系统低能有效场论

Microscopic Model versus Systematic Low-Energy Effective Field Theory for a Doped Quantum Ferromagnet

U. Gerber, C. P. Hofmann, F. Kampfer, U. -J. Wiese

摘要:

我们考虑一个微观模型的掺杂量子铁磁体作为一个测试用例的系统的低能有效场论的磁振子和空穴,这是在完全类似的情况下构建的量子反铁磁体。反铁磁体的有效场论方法只能用数值方法来检验,而在铁磁体的情况下,微观理论和有效场论都可以用解析方法来求解。通过这种方式,有效理论的低能参数通过与底层微观模型匹配而精确地确定。系统的低能有效场论准确地描述了半填充、单孔和双孔区的低能行为。特别地,对于弱束缚的两空穴态,有效场论甚至超越了微扰论。这有力地支持了系统的低能有效场论方法不仅在铁磁而且在物理上最有趣的反铁磁情况下的定量成功。

英文摘要:

We consider a microscopic model for a doped quantum ferromagnet as a test case for the systematic low-energy effective field theory for magnons and holes, which is constructed in complete analogy to the case of quantum antiferromagnets. In contrast to antiferromagnets, for which the effective field theory approach can be tested only numerically, in the ferromagnetic case both the microscopic and the effective theory can be solved analytically. In this way the low-energy parameters of the effective theory are determined exactly by matching to the underlying microscopic model. The low-energy behavior at half-filling as well as in the single- and two-hole sectors is described exactly by the systematic low-energy effective field theory. In particular, for weakly bound two-hole states the effective field theory even works beyond perturbation theory. This lends strong support to the quantitative success of the systematic low-energy effective field theory method not only in the ferromagnetic but also in the physically most interesting antiferromagnetic case.

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