格点上非相对论费米子符号问题的缓解
Mitigating the sign problem for non-relativistic fermions on the lattice
摘要：
我们研究了具有自旋独立排斥相互作用的非相对论费米子理论中的费米子符号问题。我们在动量空间中的极坐标下工作，这使得只保持低能量自由度接近费米面变得简单。这对于计算许多物理上重要的低能观测量来说是足够的。我们发现，在这个有效的理论中的符号问题将比在完整的理论弱的迹象，因此，理论的低能量属性可以通过修改的行动，使其半正定和包括重加权因子的可观测量计算。我们讨论了适当的修改的行动，并描述了一个可能的晶格实现的极动量空间制定的理论。
英文摘要：
We study the fermion sign problem in a theory of non-relativistic fermions with a spin-independent repulsive interaction. We work in polar co-ordinates in momentum space, which makes it straightforward to keep only the low-energy degrees of freedom close to the Fermi surface. This is sufficient for the purpose of calculating many physically important low-energy observables. We find indications that the sign problem in this effective theory will be weaker than in the full theory, so low-energy properties of the theory could be calculated by modifying the action to make it positive semi-definite and including reweighting factors in the observables. We discuss suitable modifications of the action, and describe a possible lattice realization of the polar momentum space formulation of the theory.
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