The Rudolf Peierls Centre for Theoretical Physics, Oxford University, Oxford OX1 3NP, United Kingdom.
Institut für Theoretische Physik, Universität Innsbruck, A-6020 Innsbruck, Austria.
Phys Rev Lett. 2013 Mar 15;110(11):115701. doi: 10.1103/PhysRevLett.110.115701. Epub 2013 Mar 13.
We consider the von Neumann and Rényi entropies of the one-dimensional quarter-filled Hubbard model. We observe that for periodic boundary conditions the entropies exhibit an unexpected dependence on system size: for L=4 mod 8 the results are in agreement with expectations based on conformal field theory, while for L=0 mod 8 additional contributions arise. We explain this observation in terms of a shell-filling effect and develop a conformal field theory approach to calculate the extra term in the entropies. Similar shell-filling effects in entanglement entropies are expected to be present in higher dimensions and for other multicomponent systems.
我们研究了一维半满 Hubbard 模型的 von Neumann 和 Rényi 熵。我们发现，对于周期性边界条件，熵表现出出乎意料的对系统大小的依赖：对于 L=4 mod 8，结果与基于共形场理论的预期一致，而对于 L=0 mod 8，会出现额外的贡献。我们根据壳层填充效应对此观察结果进行了解释，并开发了一种共形场理论方法来计算熵中的额外项。预计在更高维度和其他多分量系统中也会存在类似的纠缠熵的壳层填充效应。
